Question

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) 8.9 cm

2) 44.5 cm^2

Explanation:

a) we want to calculate the length of the arc

Mathematically, we use the formula for the length of an arc

That will be ;

theta/360 * 2 * pi * r

theta = central angle = 51

r is radius = 10 cm

so we have ;

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

2) The area of the sector is;

theta/360 * pi * r^2

51/360 * 22/7 * 10^2

= 44.5 cm^2