Question

One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?

Answer 1

The area of a circle:

`A=\pi r^2`
r - the radius, which is equal to half the diameter d

The first circle:

`d_1=6 \\ r_1=(6)/(2) = 3 \\ A_1=\pi * 3^2=9\pi`

The second circle:
the second circle has a diameter that is four times the diameter of the first circle.

`d_2=6 * 4=24 \\ r_2=(24)/(2)=12 \\ A_2=\pi * 12^2 = 144\pi`

The ratio of the area of the smaller cirlce to the area of the larger circle:

`(A_1)/(A_2)=(9 \pi)/(144 \pi)=(9)/(144)=(9 / 9)/(144 / 9)=(1)/(16)`

The ratio is 1:16.