Question

A sprinkler sprays over a distance of 40 feet and rotates through an angle of 80. Find the area watered by the sprinkler.

Answer 1

Answer:

1,115.8937105551

Step-by-step explanation:

[ π x 40² ] =5,026.5482457437

[ 80 / 360 ] ft² =[,222] ft²

5,026.5482457437 X [,222] ft²= 1,115.8937105551 ft² 

A = [ π x 40² ] [ 80 / 360 ] ft² 

A = 1,115.8937105551 ft²

Answer 2

The area watered by the sprinkler is 1117.0 sq. feet. The sprinkler sprays in a circular direction with an angle of 80° and a radius of 40 feet.

What is the area of a circle?

• The area of the circle is πr².
• If an angle of rotation is θ then the area is calculated by [θ/360]×πr².
• Where r is the radius.

Calculation:

Given that,

The sprinkler sprays over a distance of 40 feet i.e., r = 40 feet

The sprinkler rotates at an angle of 80°

So, the area watered by the sprinkler is

= $\frac{80}{360}$ × π × r²

= 0.22 × π × (40)²

= 1117.0 sq. feet

Therefore, the area is 1117.0 sq. feet.

Learn more about the area formed by an angle of rotation here:

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