Question

Carpet is to be laid in a room that is in the form of

acircular sector with a central angle of 105o. If
thelength (radius) of the room is 80 feet, what is the area of
thecarpet to be laid?

Answer 1

5,864.31 ft²

Explanation:

The area of a full circle is given by:

`A_C=\pi r^2`

Since the room is a circular sector with a central angle of 105 degrees and knowing that a circle has a central angle of 360 degrees, the area of the room is:

`A_R=(105)/(360) \pi r^2=(105)/(360) \pi 80^2\\A_R = 5,864.31\ ft^2`

The area of the carpet to be laid is 5,864.31 ft².