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
`(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
`(1)/(4)` of the entire circle. So, the area of the sector is equal to
`(1)/(4)` of the area of the entire circle.

`9\pi=(1)/(4)* \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 √(36) =r`

`\pm 6 =r`

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

Therefore, the radius of the circle is 6 cm.