Question

The radii of two circles are in the ratio of 3 to 1. Find the area of the smaller circle if the area of the larger circle is 27 pi sq. in.

Answer 1

3(pi)

Explanation:

Answer 2

ANSWER

`3\pi sq.\: in.`

EXPLANATION

Let R be the radius of the bigger circle and r, be the radius of the smaller circle.

Then their ratio is given as,


`R:r=3:1`

We can rewrite it as fractions to get,


`(R)/(r) = (3)/(1)`

We make R the subject to get,


`R = 3r`

The area of the bigger circle can be found using the formula,


`Area=\pi {r}^(2)`

This implies that,


`Area=\pi ({3r})^(2)`


`Area=9\pi {r}^(2)`

But it was given in the question that, the area of the bigger circle is 27π.


`27\pi=9\pi {r}^(2)`

We divide through by 9π to get,


`3 = {r}^(2)`

This means that,

`r = √(3)`

The area of the smaller circle is therefore


`= \pi {( √(3)) }^(2)`


`= 3\pi`