neeshaampadu
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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

Sagot :

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the Radius ~

[tex]\qquad \sf  \dashrightarrow \: area = \frac{ \theta}{360} \times \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 80= \frac{ 72}{360} \times \pi {r}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 360}{72 \times \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 5}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {r}^{} = \sqrt\frac{400}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = \frac{20}{ \sqrt{\pi} } [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:r \approx 11.28 \: ft[/tex]

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

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