Question

A spotlight has a beam that travels 100 feet and covers an area intercepted by an 84°

angle, as shown

What is area covered by the beam to the nearest square foot?
31416 satt
184 sq.ft
7330 sq.ft
26389 sq.ft

Answer 1

7330 sq.ft

Explanation:

Area covered by the beam = Area of sector

Area of sector =
`(\theta)/(360) * \pi r^2`

Where,

`\theta = 84°`

Radius (r) = 100 ft

Plug in the values into the formula

Area of sector =
`(84)/(360) * \pi 100^2`

Area of sector =
`(84 * \pi * 10,000)/(360)`

Area of sector = 7,330 ft² (nearest square foot)