Question

Please help i need this done by the next hour

The sector of a circle is shown below. It has a radius of 10 centimeters and a central
angle of 51 degrees. Find to the nearest tenth in both cases:
(a) the length of AB in centimeters(b) the area of the sector in square centimeters

Answer 1

1. 9.8 cm

2. 44.5 cm^2

Explanation:

1. To find the length of arc AB, we use the formula for the length of an arc

Mathematically, that will be;

theta/360 * 2 * pi * r

theta is the central angle which is 51

r is the radius which is 10 cm

So we have

51/360 * 2 * 22/7 * 10 = 8.9 cm

2. The area of the sector

we use the formula for the area of a sector here,

That is;

theta/360 * pi * r^2

51/360 * 22/7 * 10 * 10

= 44.5 cm^2