Chapter 11, Problem 16CT

To determine

To Find: The ratio of their radii and circumference.

Answer to Problem 16CT

  $\begin{array}{l}\frac{r_1}{r_2}=\frac{5}{3}\\ \frac{C_1}{C_2}=\frac{5}{3}\end{array}$

Explanation of Solution

Given: The area of two circles are $100\pi and36\pi$

Given: $A_1=100\pi and{A}_2=36\pi$

  $\begin{array}{l}{A}_1=\pi r_1{}^2\\ 100\pi =\pi r_1{}^2\\ r_1{}^2=100\\ r_1=10\\ similarly\\ A_1=\pi r_2{}^2\\ 36\pi =\pi r_2{}^2\\ r_2{}^2=36\\ r_2=6\\ ratio\\ \frac{r_1}{r_2}=\frac{10}{6}=\frac{5}{3}\end{array}$

Now

Ratio of circumference.

  $\begin{array}{l}{C}_1=2\pi r_1\\ C_1=2\pi (10)\\ C_1=20\pi \\ similarly\\ C_2=2\pi r_2\\ C_2=2\pi (6)\\ C_2=12\pi \\ Ratio\\ \frac{C_1}{C_2}=\frac{20\pi }{12\pi }=\frac{5}{3}\end{array}$