Question

Find the ratio of the areas of the two circles

Answer 1

`\text{ratio}=(25)/(36)`

Step-by-step explanation

the area of a circle is given by:

`\begin{gathered} \text{Area}=\text{ }\pi r^2 \\ or \\ \text{Area}=\text{ }\pi((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((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}=(100\pi)/(144\pi) \\ \text{ratio}=(50)/(72)=(25)/(36) \\ \text{ratio}=(25)/(36) \end{gathered}`

I hope this helps you