Question

In the diagram the radius of the outer circle is 2x cm and the radius of the inner circle is 6 cm. The area of the shaded region is 160

Answer 1

let's find the area of the outer circle and the inside circle

the inside's circle area

A= π x 6²=36π

the outer's

A' = π x 4x²= 4πx²

A'-A=4πx²- 36π=160πcm² equivalent to x²- 9=40, so x²=49 implies x =sqrt(49)=7, x=7.