Question

Find the volume of the space not taken up by the volleyball.

Answer 1

Given that a volleyball is shipped in the cubical box.

The diameter of the ball is = 8.15 inches

So the radius will be r = 8.15/2 inches = 4.075

Now, the diameter of the ball will be the side of the cube as it is inside the box.

Then the side of the cube is a = 8.15 inches

Hence, the volume of the cubical box will be

$\begin{gathered} V=a^3 \\ V=8.15\times8.15\times8.15\text{ in}^3 \\ V=541.343375\text{ in}^3 \end{gathered}$

Now the volume of the ball

$\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\frac{4}{3}\times3.14\times4.075\times4.075\times4.075\text{ in}^3 \\ v=283.303033 \end{gathered}$

Now the required volume will be

= V - v = 541.343375 - 283.303033 cubic inches

= 258.040342 cubic inches

After round-off, the answer will be 258 cubic inches.

Therefore the space left will be 258 cubic inches.