Question

A strawberry farmer needs to water a strawberry patch of 1500 square yards is in the shape of a sector of a circle with a radius of 40 yards. Through what angle should the sprinkler rotate

Answer 1

The sprinkler must rotate by an angle of 107.48°.

Explanation:

Given:

Area of strawberry patch( in shape of sector) = 1500 square yards

Radius of circle = 40 yards

To find angle through which the sprinkler should rotate.

Solution.

In order to find the angle of rotation of sprinkler, we will apply the area of sector formula.

`Area\ of\ sector\ = (\theta)/(360)* \pi r^2`

where
`\theta` is the angle of the sector formed and
`r` is radius of the circle.

Thus, we can plugin the given values to find
`\theta` which would be the angle of rotation.

`1500 = (\theta)/(360)* \pi (40)^2`

Taking
`\pi=3.14`

`1500 = (\theta)/(360)* \ (3.14) (40)^2`

`1500 = (\theta)/(360)* 5024`

Dividing both sides by 5024.

`(1500)/(5024) = (\theta)/(360)* 5024/ 5024`

Multiplying both sides by 360.

`(1500* 360)/(5024) =(\theta)/(360)* 360`

`107.48=\theta`

∴
`\theta= 107.48\°`

Angle of rotation of sprinkler = 107.48°