PRE-CALC COLLEGE LEVEL PLS HELP

Question

When a sprinkler is set to full rotation, the water covers a circular section of garden with radius 36 feet. If the sprinkler is set to rotate back and forth through an angle of 24°, find the area of the garden that is covered by the sprinkler.

area = ____ ft²

Answer 1

Hi Zaira, there are several ways to solve this type of problem.

1) Use the formula: Area of a sector of a circle is equal to the radius squared times the central angle divide by 2.

Area = r² * a / 2

Where r is the radius

a is the central angle

Area = 36² * 24 / 2

Area = 271.4 sq feet

2) Find out what part of the circle the central angle represents. Divide the area of the circle by this value.

Area = (π * r² ) / (360 / central angle)

Where r is the radius

Area = (3.14159 * 36²) / (360 / 24)

Area = 4069.44 / 15

Area = 271.4 sq feet

Questions?

Answer 2

the area of the entire circular region is pir^2= (36)^2pi= 1296 pi

24 degrees is 24/360 th of the entire region = 1296 pi x24/360= 86.4 pi ft^2