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larisa86 [58]
3 years ago
11

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

Mathematics
1 answer:
kap26 [50]3 years ago
6 0

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.

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