## Related questions with answers

The dart board shown is divided into twenty equal sectors. If the diameter of the board is 18 inches, what area of the board does each sector cover?

Solution

VerifiedIf the board is divided into 20 equal sectors, then the central angle of each sector has a measure of $360\text{\textdegree} \div 20=18\text{\textdegree}$. So, the measure of a sector's central angle is $18\text{\textdegree}$ and the radius is $18\div 2=9$ inches.

We convert the central angle measure to radians.

$\begin{align*} 18\text{\textdegree}&=18\text{\textdegree}(\dfrac{\pi \quad radians}{180\text{\textdegree}}) \\ &=\dfrac{\pi}{10} \end{align*}$

We use the central angle and the radius to find the area of a sector.

$\begin{align*} A&=\dfrac{1}{2}r^2\theta \\ &=\dfrac{1}{2}(9)^2(\dfrac{\pi}{10}) \\ &\approx12.7 \end{align*}$

Therefore, each sector covers an area of about 12.7 square inches.

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