Question

A sprinkler on a golf course is set to spray water over a distance of 75 feet and rotates through an angle of 135 degrees. Find the area of the fairway watered by the sprinkler

Answer 1

Answer:

6623.4375 feet²

Step-by-step explanation:

Distance is the radius

Area:

(135/360) × pi × r²

(135/360) × 3.14 × 75²

6623.4375 feet²

Answer 2

The area of the fairway watered by the sprinkler is 6,623.44 square feet

The shape of the golf course is a sector, Using the formula for calculating the area of a sector is expressed as:

$A = \frac{\theta}{360} \times \pi r^2$

• r is the radius = 75 feet

• $\theta$ is the angle subtended = $135^0$

Substitute the given parameters into the formula to have:

$A=\frac{135}{360} \times 3.14 \times 75^2 \\A = \frac{2,384,437.5}{360}\\A= 6,623.4375ft^2$

Hence the area of the fairway watered by the sprinkler is 6,623.44 square feet

Learn more on area of a sector here: https://brainly.com/question/12792310