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

Answer:

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

Step-by-step 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:

$Sector\ Area =\frac{\theta}{360^{\circ}} * \pi r^2$

Where:

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

So, we have:

$Sector\ Area =\frac{\theta}{360^{\circ}} * 240m^2$

Substitute 75 for $\theta$

$Sector\ Area =\frac{75^{\circ}}{360^{\circ}} * 240m^2$

$Sector\ Area =\frac{75^{\circ}* 240m^2}{360^{\circ}}$

$Sector\ Area =\frac{75* 240m^2}{360}$

$Sector\ Area =\frac{18000m^2}{360}$

$Sector\ Area =\frac{18000}{360} m^2$

$Sector\ Area =50m^2$

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