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olga55 [171]
3 years ago
9

Pleaseee Helpp. If the radius is 21 m and area of sector of the circle are 27.72 m2, calculate the angle at the centre of the ci

rcle.​
Mathematics
1 answer:
Butoxors [25]3 years ago
3 0

Given:

Radius of a circle = 21 m

Area of a sector of the circle = 27.72 m²

To find:

The angle at the center of the circle.​

Solution:

The area of a second is:

A=\pi r^2\times \dfrac{\theta}{360^\circ}

Where, r is the radius of the circle and \theta is the central angle.

Putting \pi=\dfrac{22}{7},\ r=21,\ A=27.72 in the above formula, we get

27.72=\dfrac{22}{7}\times (21)^2\times \dfrac{\theta}{360^\circ}

27.72=1386\times \dfrac{\theta}{360^\circ}

27.72=3.85^\circ \times \theta

\dfrac{27.72}{3.85^\circ }=\theta

7.2^\circ=\theta

Therefore, the central angle of the sector is 7.2^\circ.

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