Chapter 12.8, Problem 3CYP

To determine

Find the circumference of the children's ball.

Answer to Problem 3CYP

About 41.3 cm

Explanation of Solution

Given:

A regulation volleyball has a circumference of about 66 centimeters. The ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6: 1 .

Calculation:

Circumference of a sphere with radius r = $C=2\pi r$

Surface area of a sphere with radius r = $S=4\pi r=2\cdot 2\pi r=2C$

Given ratio of surface area :

  $\begin{array}{l}\frac{S{A}_{children\text{'}s}}{S{A}_{regulation}}=\frac{1}{1.6}=\frac{2C_{children\text{'}s}}{2C_{regulation}}\\ \Rightarrow \frac{C_{children\text{'}s}}{C_{regulation}}=\frac{1}{1.6}\\ \Rightarrow \frac{C_{children\text{'}s}}{66}=\frac{1}{1.6}\\ \Rightarrow C_{children\text{'}s}=66\times \frac{1}{1.6}\mathrm{............}[\text{multiply each side by 66]}\\ \Rightarrow C_{children\text{'}s}=41.25\end{array}$

So, the circumference of children’s ball is about 41.3 cm.