A sector of area 17 square feet is formed by a central angle of 154.6986 ∘ 154.6986∘. Find the radius of the circle?

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A sector of area 17 square feet is formed by a central angle of 154.6986 ∘ 154.6986∘. Find the radius of the circle?

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Answer 1 · 2018-02-24T22:40:59

$r = 3.5486 f t$ $color(blue)(r=3.5486ft)$

Explanation:

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In Circle $O$ $O$ , radii $O A$ $OA$ and $O C$ $OC$ enclose the sector $O A B C$ $OABC$ which has a central angle of:

$∠ A O C = {154.6986}^{\circ}$ $color(red)(/_AOC=154.6986^@)$

The area of the sector is:

$A_{sector} = 17 s q f t$ $color(red)(A_("sector")=17sqft)$

Area of the circle is:

$A_{circle} = (\frac{A_{sector}}{{154.6986}^{\circ}}) (360^{\circ}) = \frac{17}{154.6986} \cdot 360$ $A_("circle") = (A_("sector")/154.6986^@)(360^@)=17/154.6986*360$

$A_{circle} = 39.5608 s q f t$ $color(purple)(A_("circle")=39.5608sqft)$

The formula for area of a circle is $π r^{2}$ $pir^2$ where $r$ $r$ is the radius.

$π r^{2} = 39.5608$ $pir^2=39.5608$

$r^{2} = \frac{39.5608}{π} = 12.5926$ $r^2=39.5608/pi=12.5926$

$r = 3.5486 f t$ $color(blue)(r=3.5486ft)$

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A sector of area 17 square feet is formed by a central angle of 154.6986 ∘ 154.6986∘. Find the radius of the circle?

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