Question

An engineer is asked to design a water sprinkler that will cover a field of 100 square yards that is in the shape of a sector of a circle of radius 15 yards. Through what angle should the sprinkler rotate?

Answer 1

50.96 degrees

Explanation:

step 1

Find the area of complete circle with radius 15 yards

The area of the circle is given by the formula

`A=\pi r^(2)`

substitute the given value of r

`A=\pi (15)^(2)`

`A=225\pi\ yd^2`

assume

`\pi =3.14`

`A=225(3.14)=706.5\ yd^2`

step 2

Through what angle should the sprinkler rotate?

we know that

The area of the complete circle subtends a central angle of 360 degrees

so

using proportion

Find out the central angle of a sector of 100 square yards

`(706.5)/(360^o)=(100)/(x) \\\\x=360(100)/706.5\\\\x= 50.96^o`