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

Answer:

The sprinkler must rotate by an angle of 107.48°.

Step-by-step 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.

$Area\ of\ sector\ = \frac{\theta}{360}\times \pi r^2$

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.

$1500 = \frac{\theta}{360}\times \pi (40)^2$

Taking $\pi=3.14$

$1500 = \frac{\theta}{360}\times \ (3.14) (40)^2$

$1500 = \frac{\theta}{360}\times 5024$

Dividing both sides by 5024.

$\frac{1500}{5024} = \frac{\theta}{360}\times 5024\div 5024$

Multiplying both sides by 360.

$\frac{1500\times 360}{5024} =\frac{\theta}{360}\times 360$

$107.48=\theta$

∴ $\theta= 107.48\°$

Angle of rotation of sprinkler = 107.48°