Question

Find the ratio of the areas of the two circles

Answer 1

$\text{ratio}=\frac{25}{36}$

Explanation

the area of a circle is given by:

$\begin{gathered} \text{Area}=\text{ }\pi r^2 \\ or \\ \text{Area}=\text{ }\pi(\frac{D^2}{4}) \end{gathered}$

then

Step 1

find the area of the circles

a)let radius= r=10 m

replace

$\begin{gathered} \text{Area}=\text{ }\pi r^2 \\ \text{Area}=\pi(10m)^2 \\ \text{Area}=100\pi(m^2) \end{gathered}$

b) let

diameter= 24 m

replace

$\begin{gathered} \text{Area}=\text{ }\pi(\frac{D^2}{4}) \\ \text{Area}=\text{ }\pi(\frac{(24)^2^{}}{4}) \\ \text{Area}=\text{ }\pi(\frac{(24)^2^{}}{4}) \\ Area_2=144\text{ }\pi \end{gathered}$

Step 2

now, find the ratio of the areas

so

$\begin{gathered} \text{ratio}=\text{ }\frac{Area_1}{Area_2_{}} \\ \text{replace} \\ \text{ratio}=\frac{100\pi}{144\pi} \\ \text{ratio}=\frac{50}{72}=\frac{25}{36} \\ \text{ratio}=\frac{25}{36} \end{gathered}$

I hope this helps you