Question

The shaded sector above covers 1/3 of the circle. If the radius of the circle above is 3 cm, what is the area of the sector in terms of ?

Answer 1

Given:

The shaded sector above covers $\dfrac{1}{3}$ of the circle.

Radius of the circle = 3 cm

To find:

The area of the sector in terms of π.

Solution:

The area of a circle is

$A=\pi r^2$

Substituting $r=3$, we get

$A=\pi (3)^2$

$A=9\pi$

It is given that the shaded sector above covers $\dfrac{1}{3}$ of the circle.

The area of shaded sector $=\dfrac{1}{3}A$

                                             $=\dfrac{1}{3}(9\pi)$

                                             $=3\pi$

Therefore, the area of shaded sector is 3π sq. cm.