Question

14. The radius of a smaller circle is half the length of the radius of a larger circle.The area of the larger circle is 113.04 square inches. What is the approximate areaof the smaller circle?

Answer 1

Answer:

The approximate area of the smaller circle is;

$28.26\text{ }in^2$

Explanation:

Given that the radius of a smaller circle is half the length of the radius of a larger circle.

Let R and r represent the radius of the larger and smaller circle respectively;

$R=2r$

The area of the smaller circle will be;

$A_s=\pi r^2$

while the area of the larger circle will be;

$A_l=\pi R^2$

substituting R = 2r;

$\begin{gathered} A_l=\pi R^2 \\ A_l=\pi(2r)^2 \\ A_l=\pi(2^2r^2) \\ A_l=4\pi r^2 \end{gathered}$

We can now replace the area of the smaller circle;

$\begin{gathered} A_l=4\pi r^2 \\ \text{And we know that;} \\ A_s=\pi r^2 \\ so; \\ A_l=4A_s \\ \therefore \\ A_s=\frac{A_l}{4} \end{gathered}$

Given in the question;

The area of the larger circle is 113.04 square inches.

$A_l=113.04\text{ }in^2$

Substituting the area of the larger circle;

$\begin{gathered} A_s=\frac{A_l}{4} \\ A_s=\frac{113.04}{4} \\ A_s=28.26\text{ }in^2 \end{gathered}$

Therefore, the approximate area of the smaller circle is;

$28.26\text{ }in^2$