Question

A circle with area \blue{100\pi}100πstart color #6495ed, 100, pi, end color #6495ed has a sector with a central angle of \purple{\dfrac{2}{5}\pi}
5
2
​
πstart color #9d38bd, start fraction, 2, divided by, 5, end fraction, pi, end color #9d38bd radians .
What is the area of the sector?
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal

Answer 1

First, we need to find the radius from the circle with the area 100pi.
The formula for area of a circle is pi*r^2
pi*r^2= 100pi
We can eliminate the both pi since they are on both sides of the equation. This means r^2=100, and r= the square root of 100, which is 10.

Now we know the radius is 10, we can plug it into the equation for arc sector area- (n is the central angle, replace n with the central angle)
n/360 * 2*pi*r
n/360 * 2*pi*10
n/360 * 20pi

Hope this helps a bit