Question

a lawn sprinkler located at the corner of a yard is set to rotate through 90 degrees and project 30.0 feet. what area of lawn is watered by the sprinkler? round to the nearest whole

Answer 1

`A\approx 707 \ ft^2`

Explanation:

Area of a circular sector

A circular sector is defined by a central angle θ and the radius of the circle r. The area of the circular sector is:

`{\displaystyle A={\frac {r^(2)\theta }{2}}}`

Note: θ must be expressed in radians.

The lawn sprinkler rotates θ=90° to an area of radius r=30 feet.

Expressing θ in radians:

`\theta=90*\pi/180=\pi/2`

The area is:

`{\displaystyle A={\frac {30^(2)\pi/2 }{2}}}`

`A=706.9\ ft^2`

`\boxed{A\approx 707 \ ft^2}`