Answer:
- 2502.1 square inches
- $660
Step-by-step explanation:
The area of a fraction of a circle can be found by multiplying the area of the whole circle by the fraction of interest. The area of a donut can be found by subtracting the inner circle area from the outer circle area.
__
A)
There are 360° in a circle. Your figure has 280° of the circle shaded, so the shaded area is 280/360 = 7/9 of the area of the circle. The circle area is found from the formula ...
A = πr²
A = π(32 in)² = 1024π in²
Then the shaded area is ...
shaded = (7/9)(1024π in²) = 7168π/9 ≈ 2502.1 . . . square inches
__
B)
The difference in areas of the circle with radius 6.5 ft and that with radius 4 ft is ...
ΔA = π(6.5 ft)² -π(4 ft)² = π(42.25 -16) ft² = 26.25π ft²
The part of the donut of interest is 72/360 = 1/5 of the whole donut, so its area is ...
(1/5)(26.25π) ft² = 5.25π ft²
At $40 per square foot, the cost of painting will be ...
($40/ft²)×(5.25π ft²) = $210π ≈ $660
The total cost to paint the area is about $660.
