Question

What is the area of the shaded sector if the radius of circle Z is 5 inches?

Answer 1

We first calculate the area of the whole circle the formula for the area of a circle is

$A=\pi r^2$

r is the radius in this case r=5

we substitute the value

$A=\pi5^2=25\pi$

then we divide 120 between 360 in order to find the ratio of the shaded area

$\frac{120}{360}=\frac{1}{3}$

we multiply the number above by the area of the whole circle to obtain the shaded area,

$SA=25\pi\cdot\frac{1}{3}=\frac{25\pi}{3}$