Question

The diagram shows the area of a lawn covered by a water sprinklerWhat is the area of the lawn that is covered by the sprinkler? Round your answer to the nearest whole numberThe water pressure is weakened so that the radius is 12 feet? What is the area of the lawn that will be covered? Round your answer to the nearest whole number

Answer 1

The area of a circular sector with radius r and a central angle θ (in degrees) is given by the formula:

`A=\pi r^2\cdot(\theta)/(360)`

Substitute r=15ft and θ=145 to find the area covered by the sprinkler:

`\begin{gathered} A=\pi\cdot(15ft)^2\cdot(145)/(360) \\ =(725)/(8)\pi\cdot ft^2 \\ =284.71\ldots ft^2 \\ \approx285ft^2 \end{gathered}`

If the radius of the sector is 12 feet, then the area would be:

`\begin{gathered} A=\pi\cdot(12ft)^2\cdot(145)/(360) \\ =(4176)/(73)\pi\cdot ft^2 \\ =179.72\ldots ft^2 \\ \approx180ft^2 \end{gathered}`