Question

The radius of a circle is 2 miles. What is the area of a sector bounded by a 180° arc?Give the exact answer in simplest form.

Answer 1

The area of the sector is 44/7 square miles

For a circle, the total angle subtended at the center is 360

Hence, an arc that subtends an angle at the center of the circle is a semi-circle

So, by finding the area of the circle and dividing by 2, we have the area of the sector

Mathematically, we have this as;

`\text{Area = }(\pi* r^2)/(2)\text{ = }(3.142*2^2)/(2)\text{ = 2 }*\text{ 3.142 = 2}\pi\text{ or}(44)/(7)mi^2`