Question

A spherical ball with a volume of 2,304π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?

Answer 1

Answer:

Therefore the volume of the box is 13824 in³

Step-by-step explanation:

Given:

A spherical ball with is packaged in a box that is in the shape of a cube.

Volume of ball = 2304π in³.

Let 'r' be the radius of sphere

To Find:

Volume of Cube = ?

Solution:

Volume of sphere is given by

$\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}$

Substituting the values we get

$2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in$

Now we know that diameter is given by

$diameter=2\times r=2\times 12=24\ in$

it is given that,

The edge length of the box is equal to the diameter of the ball.

Therefore the length of cube = 24 in

Now the volume of the cube is given by

$\textrm{Volume of cube}=(edge)^{3}$

substituting the values we get

$\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}$

Therefore the volume of the box is 13824 in³