Question

a sector of a circle has a central angle measure of 60°, and an area of 14 sq inches, what is the area of the entire circle​

Answer 1

area of entire circle = 84 in²

Step-by-step explanation:

`\sf (\theta)/(360) *\pi *r^2 = Area \ of \ sector`

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`\sf \rightarrow (60)/(360) *\pi *r^2 = 14`

`\sf \rightarrow (1)/(6)\pi *r^2 = 14`

`\sf \rightarrow r^2 = (14*6)/( \pi)`

`\sf \rightarrow r = \sqrt{(84)/( \pi) }`

`\sf \rightarrow r = 5.17\ in`

Area of circle:

`\sf \pi r^2`

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`\hookrightarrow \sf \pi (5.17)^2`

`\hookrightarrow \sf 84\ in^2`