Question

What is the area of a sector with a central angle of 2π7 radians and a diameter of 40.6 mm?

Use 3.14 for π and round your answer to the nearest hundredth.


Enter your answer as a decimal in the box.

Answer 1

184.85 square mm

Explanation:

The area of a sector of a circle is
`(1)/(2) r^(2) \theta`, where r is the radius and
`\theta` is the angle in radians subtended by the arc at the centre of the circle.

Since, diameter = 40.6 mm

So, radius(r)=20.3 mm and
`\theta`=
`(2 \pi)/(7)` radians

So, area of sector=
`(1)/(2) r^(2) \theta`

=
`(1)/(2) (20.3)^2 ((2 * 3.14)/(7))`

=184.85 square mm