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?
The area of a circle: [tex]A=\pi r^2[/tex] r - the radius, which is equal to half the diameter d
The first circle: [tex]d_1=6 \\
r_1=\frac{6}{2} = 3 \\
A_1=\pi \times 3^2=9\pi[/tex]
The second circle: the second circle has a diameter that is four times the diameter of the first circle. [tex]d_2=6 \times 4=24 \\
r_2=\frac{24}{2}=12 \\
A_2=\pi \times 12^2 = 144\pi[/tex]
The ratio of the area of the smaller cirlce to the area of the larger circle: [tex]\frac{A_1}{A_2}=\frac{9 \pi}{144 \pi}=\frac{9}{144}=\frac{9 \div 9}{144 \div 9}=\frac{1}{16}[/tex]