Question

Determine the diameter of the circle G. The area given is the area of the shaded sector.

Answer 1

Area of the shaded figure is,

`\text{Area = }277cm^2`

The given shaded region represents the sector of a circle . The central angle covered by the given region is,

`\begin{gathered} \text{Central angle = 360 - 72} \\ \text{Central angle = 288} \end{gathered}`

Area of a sector is given as,

`\begin{gathered} \text{Area of sector = }(\theta)/(360)\text{ }*\text{ }\pi* r^2 \\ 277\text{ = }(288)/(360)\text{ }*\text{ }3.14\text{ }* r^2 \\ \end{gathered}`

The radius of the circle G is calculated as,

`\begin{gathered} r^2\text{ = }(277*360)/(288*3.14) \\ r^2\text{ = }(99720)/(904.32) \\ r^2\text{ = }110.27 \\ r\text{ = 10.5 } \end{gathered}`

The diameter of the circle G is calculated as,

`\begin{gathered} \text{Diameter = 2r} \\ \text{Diameter = 2 }*\text{ 10.5} \\ \text{Diameter = 21 }cm \end{gathered}`

Thus the diameter of the given circle is 21 cm.