Question

The sphere at the right fits snugly inside a cube with 4-in. edges. What is the approximate volume of the space between the sphere and cube?

Answer 1

As given by the question

There are given that the inside edge is 4 in.

Now,

Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube

So,

$\begin{gathered} \text{diameter}=4\text{ inches} \\ \text{radius}=\frac{dameter}{2} \\ \text{radius}=\frac{4}{2} \\ \text{radius}=2 \end{gathered}$

Then,

Volume of the sphere is given by:

$\begin{gathered} \frac{4}{3}\times\pi\times r^3=\frac{4}{3}\times3.14\times2^3 \\ =\frac{4}{3}\times3.14\times8 \\ =33.5 \end{gathered}$

And,

The volume of a cube is:

$\begin{gathered} \text{Volume of cube=side}\times side\times side \\ =4\times4\times4 \\ =64\text{ inches} \end{gathered}$

Then,

The volume of the space between the sphere and cube = 64-33.5 = 30.5.

Hence, the answer is 30.5 cube inches.