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 sq. in.

i think the answer is 6 pi
correct me if im wrong

Answer 1

\[\frac{r_2}{r_1}=3\]
\[\frac{A_2}{A_1}=\frac{r_2}{r_1}=3^2\]
\[A_2=9A_1\implies A_1=\frac{A_2}{9}=\frac{27}{9}\]

Answer 2

so it'd be 9 pi?

Answer 3

no...

Answer 4

yeah @completeidiot

Answer 5

hmmm... 3 pi..?

Answer 6

the answer will not have pi in the solution

the area of a circle is

\[A=\pi r^2\]

Jonask solved the problem by using ratios

so if we take the ratio of the larger area to the smaller area, which we will denote as A1 and A2

\[\frac{A_1}{A_2} = \frac{\pi r_1^2}{\pi r_2 ^2 }\]

then the pi cancels out

\[\frac{A_1}{A_2} = (\frac{ r_1}{r_2 })^2\]

Answer 7

since the proportion of smaller area to larger area is 1 to 9

that means the smaller area is 1/9 the area of the larger area

and since the larger area is 27

in order to solve for the smaller area, you would need to divide 27 by 9

which is also shown by Jonask

Answer 8

pi will not be part of the answer simply due to the fact that it was cancelled out when determining the ratio