Question

Please help:In the figure, the area of the shaded region is 260π cm^2. Circle centered within another circle. The region between the circles is shaded. The radius of the inner circle is x cm. The radius of the outer circle is 18 cm. What is the value of x?Enter your answer in the box. x = __ cm

Answer 1

It is given that,

`\begin{gathered} Area\text{ of the shaded region = 260}\pi\text{ cm}^2 \\ Radius\text{ of inner circle = x cm} \\ Radius\text{ of outer circle = 18 cm} \end{gathered}`

The area of the inner circle is calculated as,

`Area\text{ of inner circle = }\pi x^2`

The area of the outer circle is calculated as,

`Area\text{ of outer circle = }\pi*18^2`

The area of the shaded region is calculated as,

Area of shaded region = Area of the outer circle - Area of the inner circle

`\begin{gathered} Area\text{ of the shaded region = }\pi*18^2\text{ - }\pi* x^2 \\ Area\text{ of the shaded region = }\pi*(18^2-x^2) \\ 260*\pi\text{ = }\pi*(18^2-x^2) \\ \end{gathered}`

The radius of inner circle is calculated as,

`\begin{gathered} 260\text{ = 18}^2-x^2 \\ x^2\text{ = 324 - 260} \\ x^2=\text{ 64} \\ x\text{ = 8} \\ \end{gathered}`

Thus the value of x is 8 cm.