Question

The radius of a circle is 10 meters. What is the area of a sector bounded by a 90 degree arc?Give the exact answer in simplest form._____ square meters.(Pi or fraction)

Answer 1

Since we know a circle has 360 degrees, the sector bounded by a 90 degree arc will be a quarter of circle (360/90 = 4). Then, to calculate the area of that sector, we can calculate the total area of the circle of radius 10, and then divide it by 4.

The area of a cirlce of radius r is:

$A=\pi r^2$

Then, the area of the sector would be:

$A_s=\frac{\pi r^2}{4}$$A_s=\frac{\pi(10m)^2}{4}=\frac{100\pi}{4}m^2$$A_s=25\pi m^2$