Chapter 12.4, Problem 25WE

To determine

To find: if the student is correct.

Answer to Problem 25WE

Volume of the cylinder in terms of r is $2\pi r^3$ .

Explanation of Solution

Given information:

Four solid metal balls fit snugly inside the cylindrical can.

Calculation:

Since, the sphere with radius r is inscribed in the cylinder. Therefore,

Radius of the cylinder will be same as sphere that is r and height will be 2r.

The Volume of cylinder is given by

  $V=\pi r^{2}h$ where $r$ is the radius of the cylinder and $h$ is the height.

Since, radius of the cylinder is $r$ and height is $h=2r$ .

Therefore, volume of the cylinder is

  $\begin{array}{l}V=\pi r^2\left(2r\right)\\ V=2\pi r^3\end{array}$

Hence,

Volume of the cylinder in terms of r is $2\pi r^3$ .