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In the diagram, the radius of the outer circle is 2x em and the radius of the inside circle is 6 cm. The area of the shaded region is 220 cm? What is the value of x2​

In the diagram, the radius of the outer circle is 2x em and the radius of the inside-example-1
User Rick Falck
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1 Answer

6 votes

Answer:

Answer: 8 (second choice)

Explanation:

Area of a Circle

Given a circle of radius r, the area is calculated by the formula:


A=\pi\ r^2

There are two circles in the diagram. The outer circle has a radius of r1=2x, thus its area is:


A_1=\pi\ (2x)^2

The interior circle has a radius of r2=6 cm, thus its area is:


A_2=\pi\ 6^2=36\pi

The shaded area is obtained by subtracting A1-A2:


A=\pi\ (2x)^2-36\pi

The value of the shaded area is given as 220π cm2. Equating:


\pi\ (2x)^2-36\pi=220\pi

Dividing by π:


(2x)^2-36=220

Adding 36:


(2x)^2=220+36=256

Taking square root:


2x=√(256)=16

Dividing by 2:

x = 8 cm

Answer: 8 (second choice)

User Whitehawk
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