Question

A sector with arc measure 72º has an

area of 80 square feet. Determine
the radius of the circle.
A 18 ft
C 12 ft
B 20 ft
D 16ft

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}♨`

Let's find the Radius ~

`\qquad \sf  \dashrightarrow \: area = ( \theta)/(360) * \pi {r}^(2)`

`\qquad \sf  \dashrightarrow \: 80= ( 72)/(360) * \pi {r}^(2)`

`\qquad \sf  \dashrightarrow \: {r}^(2) = (80 * 360)/(72 * \pi)`

`\qquad \sf  \dashrightarrow \: {r}^(2) = (80 * 5)/( \pi)`

`\qquad \sf  \dashrightarrow \: {r}^{} = \sqrt(400)/( \pi)`

`\qquad \sf  \dashrightarrow \:r = (20)/( √(\pi) )`

or

`\qquad \sf  \dashrightarrow \:r \approx 11.28 \: ft`

I hope you understood the whole procedure, let me know if you have doubts ~

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