Cross Section Of A Sphere #1 The Cross-section Of A Sphere Is Always A Circle. Cross-section Is The Term For The Intersection Of A Plane Through A Solid, Which Forms A Two-dimensional .

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Cross Section Of A Sphere #1 The Cross-section Of A Sphere Is Always A Circle. Cross-section Is The Term For The Intersection Of A Plane Through A Solid, Which Forms A Two-dimensional .

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Cross

cross (krôs, kros),USA pronunciation  n., v., adj.,  -er, -est. 
n. 
  1. a structure consisting essentially of an upright and a transverse piece, upon which persons were formerly put to death.
  2. any object, figure, or mark resembling a cross, as two intersecting lines.
  3. a mark resembling a cross, usually an X, made instead of a signature by a person unable to write.
  4. the Cross, the cross upon which Jesus died.
  5. a figure of the Cross as a Christian emblem, badge, etc.
  6. the Cross as the symbol of Christianity.
  7. a small cross with a human figure attached to it, as a representation of Jesus crucified;
    crucifix.
  8. a sign made with the right hand by tracing the figure of a cross in the air or by touching the foreheard, chest, and shoulders, as an act of devotion.
  9. a structure or monument in the form of a cross, set up for prayer, as a memorial, etc.
  10. any of various conventional representations or modifications of the Christian emblem used symbolically or for ornament, as in heraldry or art: a Latin cross; a Maltese cross.
  11. the crucifixion of Jesus as the culmination of His redemptive mission.
  12. any suffering endured for Jesus' sake.
  13. the teaching of redemption gained by Jesus' death.
  14. the Christian religion, or those who accept it;
    Christianity;
    Christendom.
  15. an opposition;
    thwarting;
    frustration.
  16. any misfortune;
    trouble.
  17. a crossing of animals or plants;
    a mixing of breeds.
  18. an animal, plant, breed, etc., produced by crossing;
    crossbreed.
  19. a person or thing that is intermediate in character between two others.
  20. [Boxing.]a punch thrown across and over the lead of an opponent.
  21. a contest the result of which is dishonestly arranged beforehand.
  22. a crossing.
  23. a place of crossing.
  24. [Plumbing.]a four-way joint or connection.
  25. an actor's movement from one area of a stage to another.
  26. Also called  cross-trade. an arrangement for the simultaneous sale and purchase of a block of stock handled by a single broker.
  27. [Mach.]spider (def. 6b).
  28. (cap.) See  Southern Cross. 
  29. bear one's cross, to accept trials or troubles patiently.
  30. take the cross, to make the vows of a crusader.

v.t. 
  1. to move, pass, or extend from one side to the other side of (a street, river, etc.).
  2. to put or draw (a line, lines, etc.) across.
  3. to cancel by marking with a cross or with a line or lines (often fol. by off or out).
  4. to mark with a cross.
  5. to lie or pass across;
    intersect.
  6. to meet and pass.
  7. to transport across something.
  8. to assist or guide (a person) across a street or intersection: The guard crossed the child at the traffic light.
  9. to place in the form of a cross or crosswise.
  10. [Biol.]to cause (members of different genera, species, breeds, varieties, or the like) to interbreed.
  11. to oppose openly;
    thwart;
    frustrate.
  12. to betray;
    double-cross.
  13. to make the sign of a cross upon or over, as in devotion: to cross oneself.
  14. to set (a yard) in proper position on a mast.
  15. [Obs.]to confront in a hostile manner.

v.i. 
  1. to lie or be athwart;
    intersect.
  2. to move, pass, or extend from one side or place to another: Cross at the intersection.
  3. to meet and pass.
  4. to interbreed.
  5. [Theat.]to move from one side of the stage to the other, esp. by passing downstage of another actor.
  6. cross one's heart. See  heart (def. 22).
  7. cross one's mind. See  mind (def. 21).
  8. cross one's path. See  path (def. 6).
  9. cross over: 
    • [Biol.](of a chromosome segment) to undergo crossing over.
    • to switch allegiance, as from one political party to another.
    • to change successfully from one field of endeavor, genre, etc., to another: to cross over from jazz to rock.
    • Also,  cross over to the other side. to die;
      pass away.
  10. cross someone's palm. See  palm 1 (def. 11).
  11. cross up: 
    • to change arrangements made with;
      deceive: He crossed me up after we had agreed to tell the police the same story.
    • to confuse: I was supposed to meet him at the station, but got crossed up.

adj. 
  1. angry and annoyed;
    ill-humored;
    snappish: Don't be cross with me.
  2. lying or passing crosswise or across each other;
    athwart;
    transverse: cross timbers.
  3. involving a reciprocal action, interchange, or the like: a cross-endorsement of political candidates; cross-marketing of related services.
  4. contrary;
    opposite: They were at cross purposes with each other.
  5. adverse;
    unfavorable.
  6. crossbred;
    hybrid.
crossa•ble, adj. 
crossa•bil′i•ty, n. 

Section

sec•tion (sekshən),USA pronunciation n. 
  1. a part that is cut off or separated.
  2. a distinct part or subdivision of anything, as an object, country, community, class, or the like: the poor section of town; the left section of a drawer.
  3. a distinct part or subdivision of a writing, as of a newspaper, legal code, chapter, etc.: the financial section of a daily paper; section 2 of the bylaws.
  4. one of a number of parts that can be fitted together to make a whole: sections of a fishing rod.
  5. (in most of the U.S. west of Ohio) one of the 36 numbered subdivisions, each one square mile (2.59 sq. km or 640 acres), of a township.
  6. an act or instance of cutting;
    separation by cutting.
    • the making of an incision.
    • an incision.
  7. a thin slice of a tissue, mineral, or the like, as for microscopic examination.
  8. a representation of an object as it would appear if cut by a plane, showing its internal structure.
  9. [Mil.]
    • a small unit consisting of two or more squads.
    • Also called  staff section. any of the subdivisions of a staff.
    • a small tactical division in naval and air units.
    • a division of a sleeping car containing both an upper and a lower berth.
    • a length of trackage, roadbed, signal equipment, etc., maintained by one crew.
  10. any of two or more trains, buses, or the like, running on the same route and schedule at the same time, one right behind the other, and considered as one unit, as when a second is necessary to accommodate more passengers than the first can carry: On holidays the New York to Boston train runs in three sections.
  11. a segment of a naturally segmented fruit, as of an orange or grapefruit.
  12. a division of an orchestra or band containing all the instruments of one class: a rhythm section.
  13. [Bookbinding.]signature (def. 8).
  14. Also called  section mark. a mark used to indicate a subdivision of a book, chapter, or the like, or as a mark of reference to a footnote.
  15. [Theat.]one of a series of circuits for controlling certain lights, as footlights.
  16. shape (def. 12).

v.t. 
  1. to cut or divide into sections.
  2. to cut through so as to present a section.
  3. to make an incision.

Of

of1  (uv, ov; unstressed əv or, esp. before consonants, ə),USA pronunciation prep. 
  1. (used to indicate distance or direction from, separation, deprivation, etc.): within a mile of the church; south of Omaha; to be robbed of one's money.
  2. (used to indicate derivation, origin, or source): a man of good family; the plays of Shakespeare; a piece of cake.
  3. (used to indicate cause, motive, occasion, or reason): to die of hunger.
  4. (used to indicate material, component parts, substance, or contents): a dress of silk; a book of poems; a package of cheese.
  5. (used to indicate apposition or identity): Is that idiot of a salesman calling again?
  6. (used to indicate specific identity or a particular item within a category): the city of Chicago; thoughts of love.
  7. (used to indicate possession, connection, or association): the king of France; the property of the church.
  8. (used to indicate inclusion in a number, class, or whole): one of us.
  9. (used to indicate the objective relation, the object of the action noted by the preceding noun or the application of a verb or adjective): the ringing of bells; He writes her of home; I'm tired of working.
  10. (used to indicate reference or respect): There is talk of peace.
  11. (used to indicate qualities or attributes): an ambassador of remarkable tact.
  12. (used to indicate a specified time): They arrived of an evening.
  13. [Chiefly Northern U.S.]before the hour of;
    until: twenty minutes of five.
  14. on the part of: It was very mean of you to laugh at me.
  15. in respect to: fleet of foot.
  16. set aside for or devoted to: a minute of prayer.
  17. [Archaic.]by: consumed of worms.

Sphere

sphere (sfēr),USA pronunciation n., v.,  sphered, spher•ing. 
n. 
  1. [Geom.]
    • a solid geometric figure generated by the revolution of a semicircle about its diameter;
      a round body whose surface is at all points equidistant from the center. Equation: x2 + y2 + z2 = r2.
    • the surface of such a figure;
      a spherical surface.
  2. any rounded body approximately of this form;
    a globular mass, shell, etc.
    • a planet or star;
      heavenly body.
    • See  celestial sphere. 
    • any of the transparent, concentric, spherical shells, or layers, in which, according to ancient belief, the planets, stars, and other heavenly bodies were set.
  3. the place or environment within which a person or thing exists;
    a field of activity or operation: to be out of one's professional sphere.
  4. a particular social world, stratum of society, or walk of life: His social sphere is small.
  5. a field of something specified: a sphere of knowledge.

v.t. 
  1. to enclose in or as if in a sphere.
  2. to form into a sphere.
  3. to place among the heavenly spheres.
sphereless, adj. 
spherelike′, adj. 

The

the1  (stressed ᵺē; unstressed before a consonant ᵺə;
unstressed before a vowel ᵺē),USA pronunciation
 definite article. 
  1. (used, esp. before a noun, with a specifying or particularizing effect, as opposed to the indefinite or generalizing force of the indefinite article a or an): the book you gave me; Come into the house.
  2. (used to mark a proper noun, natural phenomenon, ship, building, time, point of the compass, branch of endeavor, or field of study as something well-known or unique):the sun;
    the Alps;
    theQueen Elizabeth;
    the past; the West.
  3. (used with or as part of a title): the Duke of Wellington; the Reverend John Smith.
  4. (used to mark a noun as indicating the best-known, most approved, most important, most satisfying, etc.): the skiing center of the U.S.; If you're going to work hard, now is the time.
  5. (used to mark a noun as being used generically): The dog is a quadruped.
  6. (used in place of a possessive pronoun, to note a part of the body or a personal belonging): He won't be able to play football until the leg mends.
  7. (used before adjectives that are used substantively, to note an individual, a class or number of individuals, or an abstract idea): to visit the sick; from the sublime to the ridiculous.
  8. (used before a modifying adjective to specify or limit its modifying effect): He took the wrong road and drove miles out of his way.
  9. (used to indicate one particular decade of a lifetime or of a century): the sixties; the gay nineties.
  10. (one of many of a class or type, as of a manufactured item, as opposed to an individual one): Did you listen to the radio last night?
  11. enough: He saved until he had the money for a new car. She didn't have the courage to leave.
  12. (used distributively, to note any one separately) for, to, or in each;
    a or an: at one dollar the pound.

Of

of1  (uv, ov; unstressed əv or, esp. before consonants, ə),USA pronunciation prep. 
  1. (used to indicate distance or direction from, separation, deprivation, etc.): within a mile of the church; south of Omaha; to be robbed of one's money.
  2. (used to indicate derivation, origin, or source): a man of good family; the plays of Shakespeare; a piece of cake.
  3. (used to indicate cause, motive, occasion, or reason): to die of hunger.
  4. (used to indicate material, component parts, substance, or contents): a dress of silk; a book of poems; a package of cheese.
  5. (used to indicate apposition or identity): Is that idiot of a salesman calling again?
  6. (used to indicate specific identity or a particular item within a category): the city of Chicago; thoughts of love.
  7. (used to indicate possession, connection, or association): the king of France; the property of the church.
  8. (used to indicate inclusion in a number, class, or whole): one of us.
  9. (used to indicate the objective relation, the object of the action noted by the preceding noun or the application of a verb or adjective): the ringing of bells; He writes her of home; I'm tired of working.
  10. (used to indicate reference or respect): There is talk of peace.
  11. (used to indicate qualities or attributes): an ambassador of remarkable tact.
  12. (used to indicate a specified time): They arrived of an evening.
  13. [Chiefly Northern U.S.]before the hour of;
    until: twenty minutes of five.
  14. on the part of: It was very mean of you to laugh at me.
  15. in respect to: fleet of foot.
  16. set aside for or devoted to: a minute of prayer.
  17. [Archaic.]by: consumed of worms.

Sphere

sphere (sfēr),USA pronunciation n., v.,  sphered, spher•ing. 
n. 
  1. [Geom.]
    • a solid geometric figure generated by the revolution of a semicircle about its diameter;
      a round body whose surface is at all points equidistant from the center. Equation: x2 + y2 + z2 = r2.
    • the surface of such a figure;
      a spherical surface.
  2. any rounded body approximately of this form;
    a globular mass, shell, etc.
    • a planet or star;
      heavenly body.
    • See  celestial sphere. 
    • any of the transparent, concentric, spherical shells, or layers, in which, according to ancient belief, the planets, stars, and other heavenly bodies were set.
  3. the place or environment within which a person or thing exists;
    a field of activity or operation: to be out of one's professional sphere.
  4. a particular social world, stratum of society, or walk of life: His social sphere is small.
  5. a field of something specified: a sphere of knowledge.

v.t. 
  1. to enclose in or as if in a sphere.
  2. to form into a sphere.
  3. to place among the heavenly spheres.
sphereless, adj. 
spherelike′, adj. 

Is

is (iz),USA pronunciation v. 
  1. 3rd pers. sing. pres. indic. of  be. 
  2. as is. See  as 1 (def. 21).

Is

is (iz),USA pronunciation v. 
  1. 3rd pers. sing. pres. indic. of  be. 
  2. as is. See  as 1 (def. 21).

The

the1  (stressed ᵺē; unstressed before a consonant ᵺə;
unstressed before a vowel ᵺē),USA pronunciation
 definite article. 
  1. (used, esp. before a noun, with a specifying or particularizing effect, as opposed to the indefinite or generalizing force of the indefinite article a or an): the book you gave me; Come into the house.
  2. (used to mark a proper noun, natural phenomenon, ship, building, time, point of the compass, branch of endeavor, or field of study as something well-known or unique):the sun;
    the Alps;
    theQueen Elizabeth;
    the past; the West.
  3. (used with or as part of a title): the Duke of Wellington; the Reverend John Smith.
  4. (used to mark a noun as indicating the best-known, most approved, most important, most satisfying, etc.): the skiing center of the U.S.; If you're going to work hard, now is the time.
  5. (used to mark a noun as being used generically): The dog is a quadruped.
  6. (used in place of a possessive pronoun, to note a part of the body or a personal belonging): He won't be able to play football until the leg mends.
  7. (used before adjectives that are used substantively, to note an individual, a class or number of individuals, or an abstract idea): to visit the sick; from the sublime to the ridiculous.
  8. (used before a modifying adjective to specify or limit its modifying effect): He took the wrong road and drove miles out of his way.
  9. (used to indicate one particular decade of a lifetime or of a century): the sixties; the gay nineties.
  10. (one of many of a class or type, as of a manufactured item, as opposed to an individual one): Did you listen to the radio last night?
  11. enough: He saved until he had the money for a new car. She didn't have the courage to leave.
  12. (used distributively, to note any one separately) for, to, or in each;
    a or an: at one dollar the pound.

For

for (fôr; unstressed fər),USA pronunciation prep. 
  1. with the object or purpose of: to run for exercise.
  2. intended to belong to, or be used in connection with: equipment for the army; a closet for dishes.
  3. suiting the purposes or needs of: medicine for the aged.
  4. in order to obtain, gain, or acquire: a suit for alimony; to work for wages.
  5. (used to express a wish, as of something to be experienced or obtained): O, for a cold drink!
  6. sensitive or responsive to: an eye for beauty.
  7. desirous of: a longing for something; a taste for fancy clothes.
  8. in consideration or payment of;
    in return for: three for a dollar; to be thanked for one's efforts.
  9. appropriate or adapted to: a subject for speculation; clothes for winter.
  10. with regard or respect to: pressed for time; too warm for April.
  11. during the continuance of: for a long time.
  12. in favor of;
    on the side of: to be for honest government.
  13. in place of;
    instead of: a substitute for butter.
  14. in the interest of;
    on behalf of: to act for a client.
  15. in exchange for;
    as an offset to: blow for blow; money for goods.
  16. in punishment of: payment for the crime.
  17. in honor of: to give a dinner for a person.
  18. with the purpose of reaching: to start for London.
  19. contributive to: for the advantage of everybody.
  20. in order to save: to flee for one's life.
  21. in order to become: to train recruits for soldiers.
  22. in assignment or attribution to: an appointment for the afternoon; That's for you to decide.
  23. such as to allow of or to require: too many for separate mention.
  24. such as results in: his reason for going.
  25. as affecting the interests or circumstances of: bad for one's health.
  26. in proportion or with reference to: He is tall for his age.
  27. in the character of;
    as being: to know a thing for a fact.
  28. by reason of;
    because of: to shout for joy; a city famed for its beauty.
  29. in spite of: He's a decent guy for all that.
  30. to the extent or amount of: to walk for a mile.
  31. (used to introduce a subject in an infinitive phrase): It's time for me to go.
  32. (used to indicate the number of successes out of a specified number of attempts): The batter was 2 for 4 in the game.
  33. for it, See  in (def. 21).

conj. 
  1. seeing that;
    since.
  2. because.

The

the1  (stressed ᵺē; unstressed before a consonant ᵺə;
unstressed before a vowel ᵺē),USA pronunciation
 definite article. 
  1. (used, esp. before a noun, with a specifying or particularizing effect, as opposed to the indefinite or generalizing force of the indefinite article a or an): the book you gave me; Come into the house.
  2. (used to mark a proper noun, natural phenomenon, ship, building, time, point of the compass, branch of endeavor, or field of study as something well-known or unique):the sun;
    the Alps;
    theQueen Elizabeth;
    the past; the West.
  3. (used with or as part of a title): the Duke of Wellington; the Reverend John Smith.
  4. (used to mark a noun as indicating the best-known, most approved, most important, most satisfying, etc.): the skiing center of the U.S.; If you're going to work hard, now is the time.
  5. (used to mark a noun as being used generically): The dog is a quadruped.
  6. (used in place of a possessive pronoun, to note a part of the body or a personal belonging): He won't be able to play football until the leg mends.
  7. (used before adjectives that are used substantively, to note an individual, a class or number of individuals, or an abstract idea): to visit the sick; from the sublime to the ridiculous.
  8. (used before a modifying adjective to specify or limit its modifying effect): He took the wrong road and drove miles out of his way.
  9. (used to indicate one particular decade of a lifetime or of a century): the sixties; the gay nineties.
  10. (one of many of a class or type, as of a manufactured item, as opposed to an individual one): Did you listen to the radio last night?
  11. enough: He saved until he had the money for a new car. She didn't have the courage to leave.
  12. (used distributively, to note any one separately) for, to, or in each;
    a or an: at one dollar the pound.

Of

of1  (uv, ov; unstressed əv or, esp. before consonants, ə),USA pronunciation prep. 
  1. (used to indicate distance or direction from, separation, deprivation, etc.): within a mile of the church; south of Omaha; to be robbed of one's money.
  2. (used to indicate derivation, origin, or source): a man of good family; the plays of Shakespeare; a piece of cake.
  3. (used to indicate cause, motive, occasion, or reason): to die of hunger.
  4. (used to indicate material, component parts, substance, or contents): a dress of silk; a book of poems; a package of cheese.
  5. (used to indicate apposition or identity): Is that idiot of a salesman calling again?
  6. (used to indicate specific identity or a particular item within a category): the city of Chicago; thoughts of love.
  7. (used to indicate possession, connection, or association): the king of France; the property of the church.
  8. (used to indicate inclusion in a number, class, or whole): one of us.
  9. (used to indicate the objective relation, the object of the action noted by the preceding noun or the application of a verb or adjective): the ringing of bells; He writes her of home; I'm tired of working.
  10. (used to indicate reference or respect): There is talk of peace.
  11. (used to indicate qualities or attributes): an ambassador of remarkable tact.
  12. (used to indicate a specified time): They arrived of an evening.
  13. [Chiefly Northern U.S.]before the hour of;
    until: twenty minutes of five.
  14. on the part of: It was very mean of you to laugh at me.
  15. in respect to: fleet of foot.
  16. set aside for or devoted to: a minute of prayer.
  17. [Archaic.]by: consumed of worms.

Through

through (thro̅o̅),USA pronunciation prep. 
  1. in at one end, side, or surface and out at the other: to pass through a tunnel; We drove through Denver without stopping. Sun came through the window.
  2. past;
    beyond: to go through a stop sign without stopping.
  3. from one to the other of;
    between or among the individual members or parts of: to swing through the trees; This book has passed through many hands.
  4. over the surface of, by way of, or within the limits or medium of: to travel through a country; to fly through the air.
  5. during the whole period of;
    throughout: They worked through the night.
  6. having reached the end of;
    done with: to be through one's work.
  7. to and including: from 1900 through 1950.
  8. by the means or instrumentality of;
    by the way or agency of: It was through him they found out.
  9. by reason of or in consequence of: to run away through fear.
  10. in at the first step of a process, treatment, or method of handling, passing through subsequent steps or stages in order, and finished, accepted, or out of the last step or stage: The body of a car passes through 147 stages on the production line. The new tax bill finally got through Congress.

adv. 
  1. in at one end, side, or surface and out at the other: to push a needle through; just passing through.
  2. all the way;
    along the whole distance: This train goes through to Boston.
  3. throughout: soaking wet through.
  4. from the beginning to the end: to read a letter through.
  5. to the end: to carry a matter through.
  6. to a favorable or successful conclusion: He barely managed to pull through.
  7. through and through: 
    • through the whole extent of;
      thoroughly: cold through and through.
    • from beginning to end;
      in all respects: an aristocrat through and through.

adj. 
  1. having completed an action, process, etc.;
    finished: Please be still until I'm through. When will you be through with school?
  2. at the end of all relations or dealings: My sister insists she's through with selfish friends.
  3. passing or extending from one end, side, or surface to the other.
  4. traveling or moving to a destination without changing of trains, planes, etc.: a through flight.
  5. (of a road, route, way, course, etc., or of a ticket, routing order, etc.) admitting continuous or direct passage;
    having no interruption, obstruction, or hindrance: a through highway; through ticket.
  6. (of a bridge truss) having a deck or decks within the depth of the structure. Cf.  deck (def. 21).
  7. of no further use or value;
    washed-up: Critics say he's through as a writer.

Which

which (hwich, wich),USA pronunciation pron. 
  1. what one?: Which of these do you want? Which do you want?
  2. whichever: Choose which appeals to you.
  3. (used relatively in restrictive and nonrestrictive clauses to represent a specified antecedent): The book, which I read last night, was exciting. The socialism which Owen preached was unpalatable to many. The lawyer represented five families, of which the Costello family was the largest.
  4. (used relatively in restrictive clauses having that as the antecedent): Damaged goods constituted part of that which was sold at the auction.
  5. (used after a preposition to represent a specified antecedent): the horse on which I rode.
  6. (used relatively to represent a specified or implied antecedent) the one that;
    a particular one that: You may choose which you like.
  7. (used in parenthetic clauses) the thing or fact that: He hung around for hours and, which was worse, kept me from doing my work.
  8. [Nonstandard.]who or whom: a friend which helped me move; the lawyer which you hired.

adj. 
  1. what one of (a certain number or group mentioned or implied)?: Which book do you want?
  2. whichever;
    any that: Go which way you please, you'll end up here.
  3. being previously mentioned: It stormed all day, during which time the ship broke up.

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