1 Answer

Jmdon · Answer 1 · 2022-01-28T09:28:37+0000

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.

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