Question

Find r if 0=pi/6 rad sector 64m^2

Answer 1

Given:

Area of a sector = 64 m²

The central angle is $\theta=\dfrac{\pi}{6}$.

To find:

The radius or the value of r.

Solution:

Area of a sector is:

$A=\dfrac{1}{2}r^2\theta$

Where, r is the radius of the circle and $\theta$ is the central angle of the sector in radian.

Putting $A=64,\theta=\dfrac{\pi}{6}$, we get

$64=\dfrac{1}{2}r^2\times \dfrac{\pi}{6}$

$64=\dfrac{\pi}{12}r^2$

$64\times \dfrac{12}{\pi}=r^2$

$\dfrac{768}{\pi}=r^2$

Taking square root on both sides, we get

$\sqrt{\dfrac{768}{\pi}}=r$

$16\sqrt{\dfrac{3}{\pi}}=r$

Therefore, the value of r is $16\sqrt{\dfrac{3}{\pi}}$ m.