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 sprin…

Question

asked Jun 28, 2020 175k views

1 Answer

Shigeo · Answer 1 · 2020-07-05T03:33:07+0000

Answer:

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
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°