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The radius of a circle is 4 centimeters. What is the area of a sector bounded by a 72° arc?Give the exact answer in simplest form. ____ square centimeters.
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The radius of a circle is 4 centimeters. What is the area of a sector bounded by a 72° arc?Give the exact answer in simplest form. ____ square centimeters.

The radius of a circle is 4 centimeters. What is the area of a sector bounded by a-example-1
User BurtK
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1 Answer

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The formula for the area of a sector is given as


\begin{gathered} \text{Area of a sector=}(\theta)/(360)*\pi r^2 \\ \text{where,} \\ \theta=\sec toralangle=72^0 \\ r=\text{radius}=4\operatorname{cm} \end{gathered}

By substitution,


\begin{gathered} \text{Area of sector= }(72^0)/(360^0)*\pi*(4\operatorname{cm})^2 \\ \text{Area of sector=}\frac{\text{72}*\pi*16\operatorname{cm}^2}{360} \\ \text{Area of sector}=\frac{1152\pi\operatorname{cm}^2}{360} \\ \text{Area of sector}=10.053\operatorname{cm}^2 \end{gathered}

Hence,

The area of the sector=10.053 square centimeters

User Vinit Kadam
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