Chapter 12.4, Problem 24WE

To determine

To find: if the student is correct.

Answer to Problem 24WE

The student is correct.

Explanation of Solution

Given information:

Four solid metal balls fit snugly inside the cylindrical can.

Calculation:

From the given figure.

Radius of the spherical ball is r.

Radius of the cylinder is r. and

The height of the cylinder will be 8r

The Volume sphere is given by

  $V=\frac{4}{3}\pi r^3$ where $r$ is the radius of the sphere.

And, 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 8r.

Therefore, volume of the cylinder is

  $\begin{array}{l}{V}_c=\pi r^2\left(8r\right)\\ V_c=8\pi r^3\end{array}$........(1)

Now, radius of the spherical ball is r.

Therefore, volume of the ball is

  $V_b=\frac{4}{3}\pi r^3$

Volume of the 6 balls will be

  $\begin{array}{l}{V}_b=6\times \frac{4}{3}\pi r^3\\ V_b=8\pi r^3\end{array}$........(2)

From equation (1) and (2) the volume of the cylinder and 6 ball are equal.

Hence,

The student is correct.