Question

Calculate the area of a circle of radius 7cm. One sector of this circle has an area of 49.5cm^2

What is the angle at the centre of this?

Answer 1

115° 71"

Explanation:

Area of circle:

r = 7 cm

`\sf \boxed{Area \ of \ circle = \pi r^2}`

`\sf = (22)/(7)*7*7`

= 22 *7

= 154 square cm.

`\sf \boxed{Area \ of \ circle = (\theta)/(360)*\pi r^2}`

`\sf (\theta)/(360)*\pi r^2=49.5 \ cm^2`

`\sf (\theta)/(360)*(22)/(7)*7*7=49.5\\\\(\theta)/(360)*22*7 = 49.5\\`

`\sf \theta = (49.5*360)/(22*7)\\\\`

= 115° 71"