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

Answer:

184.85 square mm

Step-by-step explanation:

The area of a sector of a circle is $\frac{1}{2} r^{2} \theta$, 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  $\theta$=$\frac{2 \pi}{7}$ radians

So, area of sector= $\frac{1}{2} r^{2} \theta$

=$\frac{1}{2} (20.3)^2 (\frac{2 \times 3.14}{7})$

=184.85 square mm