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.
