Final answer:
The area of a sector of a circle with a 20 feet diameter and a π/4 radian angle is approximately 39 feet², considering significant figures.
Step-by-step explanation:
To find the area of a sector of a circle with a diameter of 20 feet and an angle of π/4 radians, we first need to find the radius. The radius (r) is half of the diameter, hence r = 20 feet / 2 = 10 feet. The area (A) of a circle is πr², which applies to the entire circle. As we are interested in a sector, we must adjust this formula to cater for the angle of the sector. The formula for the area of a sector is (n/2π) times the area of the full circle, where n is the central angle in radians.
In this case, the angle is π/4 radians, so the formula becomes:
A_sector = (π/4) / (2π) * π * (10 feet)²
= (1/8) * π * 100 feet²
= 12.5π feet²
If we use π ≈ 3.14159, the area of the sector approximates to:
A_sector ≈ 12.5 * 3.14159 feet²
= 39.27 feet²
However, we must consider significant figures in our final answer. Since the radius was given with two significant figures, our answer should reflect this precision:
A_sector ≈ 39 feet² (to two significant figures)