Answer:
(a) Area is about 285 square feet
(b) Percentage decrease = 36%
Explanation:
(a) The formula for area of a sector in degrees is
A = (θ/360º) × πr^2, where
- A is the area in square units,
- θ is the measure of the sector in degrees,
- and r is the radius
Since we're shown that the measure of the sector is 145º and the radius is 15 feet, we can plug these in for θ and r in the area formula:
A = (145/360) * π(15)^2
A = (29/72) * 225π
A = (725/8)π
A = 284.7068342
A ≈ 285 square feet
Thus, the area of the sector is about 285 square feet.
(b)
Step 1: First, we'll need to find the area of the sector if the radius was decreased to 12 feet. And since we rounded to the nearest whole number for (a), we can do that again at the end:
A = (145/360) * π(12)^2
A = (29/72) * 144π
A = 58π
A = 182.2123739
A ≈ 182 square feet
Thus, the area of the sector if the radius was decreased to 12 feet would be about 182 square feet.
Step 2: To find the percentage decrease, we can use the formula:
((starting value - ending value) / starting value) * 100. Our starting value is 285, whereas our ending value is 182:
% decrease = ((285 - 182) / 285) * 100
% decrease = (103 / 285) * 100
% decrease = 36.140
% decrease = 36
Thus, the percentage decrease from changing the radius from 15 feet to 12 feet is 36%