Question

Circle A is shown with a central angle marked 40 degrees and the radius marked 15 inches. Which of the following could be used to calculate the area of the sector in the circle shown above?

Answer 1

Alright, lets get started :

The area of sector is = 1/2 θ r^2 where θ is in radians

So lets first change our given angle θ ie 40 degree into radian.

For changing degree to radian, we multiply 40 * Pi/180 = 0.698 radians

Now lets plug the value in formula

Area = 1/2 θ r^2

Area = 1/2 * 0.698 * 15^2

Area = 78.54 square inches : Answer

Hope that will help :)

Answer 2

In degrees, the area of a sector is

$A=\frac{\theta}{360}*\pi r^2$

Since our central angle is 40 degrees, and our radius is 15, our formula will look like this:

$A=\frac{40}{360}*(15)^2\pi$ and

$A=\frac{40}{360}*225\pi$. Not sure how far you need to go with this as far as reducing or solving, but that's the formula. The actual area is $\frac{225\pi}{9}$, or in decimal form 78.54 rounded