Question

The area of a sector is 9pi cm^2 . The sector cover 1/4 of the entire circle. Find the radius of the circle. Thank you.

Answer 1

Given:

The area of a sector = $9\pi\text{cm}^2$

The sector cover $\dfrac{1}{4}$ of the entire circle.

To find:

The radius of the circle.

Solution:

Let r be the radius of the circle. Then, the area of the circle is:

$A=\pi r^2$

It is given that the sector cover $\dfrac{1}{4}$ of the entire circle. So, the area of the sector is equal to $\dfrac{1}{4}$ of the area of the entire circle.

$9\pi=\dfrac{1}{4}\times \pi r^2$

Multiply both sides by 4.

$36\pi =\pi r^2$

Divide both sides by $\pi$.

$36 =r^2$

Taking square root on both sides.

$\pm \sqrt{36} =r$

$\pm 6 =r$

Radius of a circle cannot be negative. So, $r=6$.

Therefore, the radius of the circle is 6 cm.