Question

A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphere that can be packed inside the cube shaped box? Give you answer rounded to the nearest whole cubic inch

Answer 1

6283 in³

Explanation:

The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.

Since the cardboard box is in the shape of a cube, its volume V = L³

So, L = ∛V

Since V = 12000 in³,

L = ∛(12000 in³)

L= 22.89 in

So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2

So, V = 4π(L/2)³/3

= 4πL³/8 × 3

= πL³/2 × 3

= πL³/6

= πV/6

= π12000/6

= 2000π

= 6283.19 in³

≅ 6283.2 in³

= 6283 in³ to the nearest whole cubic inch