Respuesta :
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
[tex]\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}[/tex]
Substituting the values we get
[tex]2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in[/tex]
Now we know that diameter is given by
[tex]diameter=2\times r=2\times 12=24\ in[/tex]
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
[tex]\textrm{Volume of cube}=(edge)^{3}[/tex]
substituting the values we get
[tex]\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}[/tex]
Therefore the volume of the box is 13824 in³
