Question

In the diagram, the radius of the outer circle is

Answer 1

the value of x is 8 cm.

Step-by-step explanation:

Correct Question : In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 220π cm2. What is the value of x? Enter your answer in the box.

We have ,

the area of a circle =  πr²

the outer circle area = $\pi(2x)^2 =4\pi x^2$

the inside circle area = $\pi (6)^2= 36\pi$

According to Question,

the outer circle area - the inside circle area = he shaded region

⇒ $\pi (4x^2)-36\pi =220\pi$

⇒ $x^2-9 =55$

⇒ $x^2=64$

⇒$x =\sqrt{64}=8$

Therefore , the value of x is 8 cm.