Chapter 7, Problem 14CT

(a)

To determine

To Write: The expression for the height $h$ of the can in terms of the radius $r$ then rewrite the formula for the volume of a cylinder in terms of $r$ only.

Answer to Problem 14CT

  $V=6\pi r^3$

Explanation of Solution

Given: Three tennis Balls fits tightly in a can as shown.

  

The height of the one ball is double of radius.

Therefore the height of can

  $\begin{array}{l}h=2r+2r+2r\\ h=6r\end{array}$

Now

Volume of cylinder

  $\begin{array}{l}V=\pi r^{2}h\\ h=6r\\ V=\pi r^{2}6r\\ V=6\pi r^3\end{array}$

Hence, $V=6\pi r^3$

(b)

To determine

To Find: The percent of can’s volume that is not occupied by the tennis balls.

Answer to Problem 14CT

  $2\pi r^3$

Explanation of Solution

Given: Three tennis Balls fits tightly in a can as shown.

  

Leftover volume =Volume of balls-three times volume of sphere.

i.e.

  $\begin{array}{l}=6\pi r^3-3\left(\frac{4}{3}\pi r^3\right)\\ =6\pi r^3-4\pi r^3\\ =2\pi r^3\end{array}$

Hence, $2\pi r^3$