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sweet-ann [11.9K]
3 years ago
5

Please help asap!!!!!!!!!!!

Mathematics
2 answers:
Bas_tet [7]3 years ago
7 0

ANSWER

16\pi \: sq.in

EXPLANATION

The area of a sector is calculated using the formula,

Area =  \frac{arc \: measure}{360 \degree}  \times \pi {r}^{2}

The arc measure is given as 45°

The radius of the circle is 8 inches.

We substitute to obtain,

Area =  \frac{45 \degree}{360 \degree}  \times \pi  \times {8}^{2}

Area =  \frac{1}{4}  \times 64\pi  = 16\pi

MrRa [10]3 years ago
5 0
<h2>Hello!</h2>

The answer is:

The correct option is the second option:

SectorArea=8\pi in^{2}

<h2>Why?</h2>

To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°

Calculating the total area, we have:

TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}

Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:

SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}

Hence, we have that the correct option is the second option:

SectorArea=8\pi in^{2}

Have a nice day!

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