Answer:
Answer: 8 (second choice)
Step-by-step explanation:
Area of a Circle
Given a circle of radius r, the area is calculated by the formula:
[tex]A=\pi\ r^2[/tex]
There are two circles in the diagram. The outer circle has a radius of r1=2x, thus its area is:
[tex]A_1=\pi\ (2x)^2[/tex]
The interior circle has a radius of r2=6 cm, thus its area is:
[tex]A_2=\pi\ 6^2=36\pi[/tex]
The shaded area is obtained by subtracting A1-A2:
[tex]A=\pi\ (2x)^2-36\pi[/tex]
The value of the shaded area is given as 220π cm2. Equating:
[tex]\pi\ (2x)^2-36\pi=220\pi[/tex]
Dividing by π:
[tex](2x)^2-36=220[/tex]
Adding 36:
[tex](2x)^2=220+36=256[/tex]
Taking square root:
[tex]2x=\sqrt{256}=16[/tex]
Dividing by 2:
x = 8 cm
Answer: 8 (second choice)
