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:
$d_1=6 \\ r_1=\frac{6}{2} = 3 \\ A_1=\pi \times 3^2=9\pi$

The second circle:
the second circle has a diameter that is four times the diameter of the first circle.
$d_2=6 \times 4=24 \\ r_2=\frac{24}{2}=12 \\ A_2=\pi \times 12^2 = 144\pi$

The ratio of the area of the smaller cirlce to the area of the larger circle:
$\frac{A_1}{A_2}=\frac{9 \pi}{144 \pi}=\frac{9}{144}=\frac{9 \div 9}{144 \div 9}=\frac{1}{16}$

The ratio is 1:16.