Question

What is the volume of the empty space inside the container?

Answer 1

Given:

The diameter of the ball is 2.5inches.

So the radius is

`r=1.25in`

The height of the cylinder is,

`\begin{gathered} h=3*2.5 \\ =7.5in \end{gathered}`

Required:

To find the Volume of the empty space.

Step-by-step explanation:

Now the volume of the one ball is,

`\begin{gathered} V=(4)/(3)\pi r^3 \\ \\ =(4)/(3)\pi(1.25)^3 \\ \\ =2.6041in^3 \end{gathered}`

Now the volume of the three ball is,

`\begin{gathered} V=3*2.6041 \\ =7.8125in^3 \end{gathered}`

The volume of the cylinder is,

`\begin{gathered} V=\pi r^2h \\ =\pi*1.25^2*7.5 \\ =11.71875\pi in^3 \end{gathered}`

The volume of the empty space is = volume of the cylinder - volume of the balls.

`\begin{gathered} =11.71875\pi-7.8125\pi \\ =3.91\pi in^3 \end{gathered}`

Final Answer:

Volume of the empty space is

`3.91\pi in^3`