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 = [tex]\pi(2x)^2 =4\pi x^2[/tex]
the inside circle area = [tex]\pi (6)^2= 36\pi[/tex]
According to Question,
the outer circle area - the inside circle area = he shaded region
⇒ [tex]\pi (4x^2)-36\pi =220\pi[/tex]
⇒ [tex]x^2-9 =55[/tex]
⇒ [tex]x^2=64[/tex]
⇒[tex]x =\sqrt{64}=8[/tex]
Therefore , the value of x is 8 cm.