Question

An artisan is creating a circular street mural for an art festival. The mural is going to be 50 feet wide. One sector of the mural spans 38 degrees. What is the area of the sector to the nearest square foot?

Answer 1

207 square feet.

Explanation:

The mural is going to be 50 feet wide. Means the diameter will be 50 feet.

So, the radius will be
`50/2=25` feet

One sector of the mural spans 38 degrees.

The ratio of the area of a sector to the area of the full circle equals the ratio of the degree measure of the given arc to 360.

Area =
`(38)/(360) \pi r^(2)`

=
`(38)/(360)*3.14*(25)^(2)`

= 207.15 square feet

To the nearest will be 207 square feet.

Answer 2

Using formula: A=Pi*r^2
A would represent the area of the whole mural but we would plug in r as 25, 50 is the whole width half of it is 25 which is the radius. the whole circle has a degree of 360 but we need the area of 38 degree.

A=38/360*pi*25^2
=16.57