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How to solve for the following. find the radiusA. 283.30mB. 23.80mC. 16.83mD. 11.90m

How to solve for the following. find the radiusA. 283.30mB. 23.80mC. 16.83mD. 11.90m-example-1

1 Answer

4 votes

From the given information, we need to find the radius of the circle. The area sector formula given by


A=(1)/(2)r^2\text{ }\theta

where A is the sector area, r is the radius of the circle and theta is the central angle in radians.

By substituting the given values into the formula, we have


89=(1)/(2)r^2\cdot(\pi)/(5)

which is equivalen to


89=(1)/(10)\pi r^2

Then, by multiplying both sides by 10, we have


890=\pi\cdot r^2

and by dividing both sides by Pi, we get


\begin{gathered} (890)/(\pi)=r^2 \\ \text{or equivalently,} \\ (890)/(3.1416)=r^2 \end{gathered}

which gives


\begin{gathered} 283.2951=r^2 \\ or\text{ equivalently,} \\ r^2=283.2951 \end{gathered}

Finally, by taking square root to both sides, we have


r=\sqrt[]{283.2951}

so, the radius is


r=16.83\text{ meters}

Therefore, the answer is option C

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