Final answer:
To find the area of the sector with a 14 feet diameter and angle of 3π /5 radians, we calculate the radius (7 feet) and use the formula A = (θ / 2π) ∙ πr² to find the area to be approximately 29.4 square feet, which we round to 29 square feet due to significant figures.
Step-by-step explanation:
The question asks to find the area of the sector of a circle with a diameter of 14 feet and an angle of 3π /5 radians.
To find the area of the sector, we first need to determine the radius of the circle, which is half of the diameter. Since the diameter is 14 feet, the radius (r) is 7 feet. Then, we use the formula for the area of a sector, which is A = (θ / 2π) ∙ πr², where θ is the angle of the sector in radians.
Substituting the values we have:
- r = 7 feet
- θ = 3π /5 radians
The formula becomes:
A = (3π /5 / 2π) ∙ π ∙ 7²
A = (3/5) ∙ π ∙ 49
A = 3 ∙ 49 / 5
A ≈ 147 / 5
A ≈ 29.4 square feet
We round the area to two significant figures because the radius was given to two significant figures, so the final answer is
A = 29 square feet.