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MATH / The length of the diameter of this spherical ball is equal to the height of the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 30 cm. How many cubic centimeters of the box are not occupied by the solid sphere? Express your answer in terms of π\pi. [asy] draw(Circle((7.5,7.5),5)); draw((7.5,6.2)..(2.5,7.5)--(12.5,7.5)..cycle); draw((7.5,8.8)..(2.5,7.5)--(12.5,7.5)..cycle,linetype("2 4")); fill((2.6,7.4)--(2.6,7.6)--(12.4,7.6)--(12.4,7.4)--cycle,white); dot((7.5,7.5)); draw((0,0)--(10,0)--(10,10)--(0,10)--cycle); draw((0,10)--(5,15)--(15,15)--(10,10)); draw((15,15)--(15,5)--(10,0)); draw((0,0)--(5,5)--(15,5),dashed); draw((5,5)--(5,15),dashed); [/asy]
Plain-text mathematical notation (without MathML)
The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 30 cm. How many cubic centimeters of the box are not occupied by the solid sphere? Express your answer in terms of π. [asy]
draw(Circle((7.5,7.5),5));
draw((7.5,6.2)..(2.5,7.5)--(12.5,7.5)..cycle);
draw((7.5,8.8)..(2.5,7.5)--(12.5,7.5)..cycle,linetype("2 4"));
fill((2.6,7.4)--(2.6,7.6)--(12.4,7.6)--(12.4,7.4)--cycle,white);
dot((7.5,7.5));
draw((0,0)--(10,0)--(10,10)--(0,10)--cycle);
draw((0,10)--(5,15)--(15,15)--(10,10));
draw((15,15)--(15,5)--(10,0));
draw((0,0)--(5,5)--(15,5),dashed); draw((5,5)--(5,15),dashed);
[/asy]
Original LaTeX notation
The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 30 cm. How many cubic centimeters of the box are not occupied by the solid sphere? Express your answer in terms of $\pi$. [asy]
draw(Circle((7.5,7.5),5));
draw((7.5,6.2)..(2.5,7.5)--(12.5,7.5)..cycle);
draw((7.5,8.8)..(2.5,7.5)--(12.5,7.5)..cycle,linetype("2 4"));
fill((2.6,7.4)--(2.6,7.6)--(12.4,7.6)--(12.4,7.4)--cycle,white);
dot((7.5,7.5));
draw((0,0)--(10,0)--(10,10)--(0,10)--cycle);
draw((0,10)--(5,15)--(15,15)--(10,10));
draw((15,15)--(15,5)--(10,0));
draw((0,0)--(5,5)--(15,5),dashed); draw((5,5)--(5,15),dashed);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
9e0aba64-9503-5a20-9279-4d78eaa6d463
task_key
geometry--test--9e0aba64-9503-5a20-9279-4d78eaa6d463
task_revision_id
1
config / split
geometry / test

Official source

initial import