Question

A sphere sits inside a cube and touches each
side. The cube is 10 feet on each side.
What is the volume of the cube surrounding
the sphere to the nearest tenth?

Answer 1

Answer:

Step-by-step explanation:

side of cube=10 ft

volume of cube=10³=1000 ft³

diameter of sphere=10 ft

radius of sphere=10/2=5 ft

volume of cube=(4/3)πr³=(4/3)π×5³=500 π/3

reqd. volume=1000-500 π/3=500(2-π/3)=500(6-π)/3≈476.40 ft³

Answer 2

The volume of the cube is the amount of space in the cube, and the volume of the cube surrounding the sphere is 738.2 ft³

How to determine the volume surrounding the cube?

The length of the cube is given as:

Length = 10 feet

The volume is calculated as:

V = L³

So, we have:

V = 10³

V = 1000 ft³

Also, the diameter of the sphere is:

d = 10

The volume of the sphere is then calculated as:

V = 2/3π(d/2)³

So, we have:

V = 2/3π * (10/2)³

Evaluate

V = 261.80

Calculate the difference in the volumes

d = 1000 - 261.80

Evaluate

d = 738.2

Hence, the volume of the cube surrounding the sphere is 738.2 ft³

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