Find the area of each sector. Round to the nearest hundredth place

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asked Oct 17, 2023 148k views

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Joshua Dyck · Answer 1 · 2023-10-20T23:56:54+0000

The formula to find the area of a circular sector if the angle is given in degrees is

$\text{ Area of sector }=\frac{\theta}{360\text{\degree}}\cdot\pi r^2$

Where

So, for the area of the white circular sector you have:

$\begin{gathered} \theta=32\text{\degree} \\ r=27.1\operatorname{mm} \\ \text{ Area of sector white }=\frac{32\text{\degree}}{360\text{\degree}}\cdot\pi(27.1mm)^2 \\ \text{ Area of sector white }=(4)/(45)\cdot\pi\cdot(27.1)^2mm^2 \\ \text{ Area of sector white }=(4)/(45)\cdot\pi\cdot734.41mm^2 \\ \text{ Area of sector white }=205.09mm^2 \end{gathered}$

And for the area of the gray circular sector you have:

$\begin{gathered} \theta=360\text{\degree}-32\text{\degree}=328\text{\degree} \\ r=27.1\operatorname{mm} \\ \text{ Area of sector gray }=\frac{328\text{\degree}}{360\text{\degree}}\cdot\pi(27.1mm)^2 \\ \text{ Area of sector gray }=(41)/(45)\cdot\pi\cdot(27.1)^2mm^2 \\ \text{ Area of sector gray }=(41)/(45)\cdot\pi\cdot734.41mm^2 \\ \text{ Area of sector gray }=2102.13mm^2 \end{gathered}$

Find the area of each sector. Round to the nearest hundredth place-example-1

Find the area of each sector. Round to the nearest hundredth place

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