Mathematics: 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

A sector with arc measure 72º has an area of 80 square

jaylen63

05.04.2022

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

Let's find the Radius ~

$\qquad \sf \dashrightarrow \: area = \frac{ \theta}{360} \times \pi {r}^{2}$

$\qquad \sf \dashrightarrow \: 80= \frac{ 72}{360} \times \pi {r}^{2}$

$\qquad \sf \dashrightarrow \: {r}^{2} = \frac{80 \times 360}{72 \times \pi}$

$\qquad \sf \dashrightarrow \: {r}^{2} = \frac{80 \times 5}{ \pi}$

$\qquad \sf \dashrightarrow \: {r}^{} = \sqrt\frac{400}{ \pi}$

$\qquad \sf \dashrightarrow \:r = \frac{20}{ \sqrt{\pi} }$

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

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

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crazymadhatter0

19.02.2021

63.8%

Step-by-step explanation:

638/1000 × 100

63.8%

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