Question

The shaded area in the circle below represents a damaged section of a 6-foot diameter tabletop.What value is closest to the area of the damaged section?A. 4.0 square feetB. 8.1 square feetC. 7.7 square feetD. 6.0 square feet

Answer 1

The rule of the area of the sector is

$A=\frac{\emptyset}{360}\times\pi\text{ }\times r^2$

The angle is 77 degrees

The diameter is 6 feet

The radius is half the diameter, then

The radius = 6/2 = 3 feet

Substitute the values of the angle and the radius in the rule above

$A=\frac{77}{360}\times\pi\times(3)^2=6.0475658=6.0\text{ square f}eet$

So the answer is D

The area of the damaged section is 6.0 square feet