Question

A rotating sprinkler head sprays water as far as 20 feet. the head is set to cover a central angle of . what area of grass will be watered?

Answer 1

The area of the grass that will be watered is given by  800/9 pi ft^2.

What is the area of a circle?

• Area of a circle is the region occupied by the circle in a two-dimensional plane.
• It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle.
• The unit of area is the square unit, such as m2, cm2, etc. Area of Circle = πr2 or πd2/4, square units. where π = 22/7 or 3.14.

The area of a circle of radius r is given by:

A = πr²

In this problem, a rotating sprinkler head sprays water as far as 20 feet, hence the radius is of r = 20 ft.

It covers a central angle of 80º, while an entire circle has 360º, hence the area of grass that will be watered corresponds to 80/360 = 2/9 of the area of the circle.

Hence the watered area in ft² is given by-

A = 2/9 π × (20)²

   = 800π/ 9

Therefore, the area of the grass that will be watered is given by  800/9 pi ft^2.

Learn more about area of a circle

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