Question

The total circular area a sprinkler can water is 240 2 . The sprinkler is set to rotate back and forth in a 75° pattern. Find the amount of area that will get watered.

Answer 1

The sprinkler will cover an area of
`50m^2`

Explanation:

Given

`Area = 240m^2`

`\theta = 75^(\circ)`

Required

Determine the amount of area it can cover

The amount of area is calculated by calculating the area of a sector using:

`Sector\ Area =(\theta)/(360^(\circ)) * \pi r^2`

Where:

`Area = \pi r^2 = 240m^2`

So, we have:

`Sector\ Area =(\theta)/(360^(\circ)) * 240m^2`

Substitute 75 for
`\theta`

`Sector\ Area =(75^(\circ))/(360^(\circ)) * 240m^2`

`Sector\ Area =(75^(\circ)* 240m^2)/(360^(\circ))`

`Sector\ Area =(75* 240m^2)/(360)`

`Sector\ Area =(18000m^2)/(360)`

`Sector\ Area =(18000)/(360) m^2`

`Sector\ Area =50m^2`

Hence, the sprinkler will cover an area of
`50m^2`