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…

Question

asked Sep 24, 2021 180k views

1 Answer

Pooja Aggarwal · Answer 1 · 2021-09-29T08:31:18+0000

Answer:

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)