Question

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

Answer 1

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,

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

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

Answer 2

Hello!

The answer is:

The correct option is the second option:

$SectorArea=8\pi in^{2}$

Why?

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!