Question

A sprinkler head had a 90-degree rotation and shoots 15 feet long. How much area is covered if there are 12 90-degree heads in one yard? How many 90-degree head do you need to cover a 1200 square foot yard?

Answer 1

Answer:

A) It can shoot 15 feet long and has a rotation of 90 degrees.

We can write this area:

Area = Angle*radius^2

The radius is 15 ft.

The angle must be written in radians, so we need to writhe 90° in radians.

180° is equal to pi.

Then 90° = (90°/180°)*pi = pi/2  

where pi = 3.14

Then our area is:

A = (3.14/2)*(15ft)^2 = 353.25 ft^2

B) If we have 12 of those in one yard, we can cover 12 times that area; this is:

A = 12*(353.25 ft^2) = 4239 ft^2

C) Now we want to find the angle such that the covered area for one sprinkler is equal to 1200 ft^2

Then we can replace it in the equation for the area and get:

1200ft^2 = angle*(15ft)^2 = angle*225 ft^2

angle = 1200/225 = 5.33

But this is in radians, so we may convert it to degrees.

We know that 3.14 = 180°

Then we have

5.33 rads = (5.33/3.14)*180° = 305.5°