Question

Need help on geometry please right answer only I’m giving out 40 points

Answer 1

The garden at the Skyview office park has a water fountain at the center. The sidewalk aroung the fountain is 10 feet, what is the area of the sidewalk?

392.699 square feet
235.619 square feet
78.54 square feet
706.858 square feet

Solution:
Area of the Sidewalk = Area of the outer circle - Area of the inner
Consider the area of a circle:
Area of a circle = π × r²

Area of the outer Circle= π × (10+5)²
Area of the outer Circle= 706.86 square feet

Area of the inner circle= π × (10)²
Area of the inner circle= 314.16 square feet

Area of the Sidewalk = Area of the outer circle - Area of the inner
Area of the Sidewalk = 706.86 square feet - 314.16 square feet
Area of the Sidewalk = 392.7 square feet

Answer 2

Answer: first option 392.699 square feet.


Step-by-step explanation:

1) The shape of the sidewalk is an ring with exterior radius equal to the radious of the fountain + 5 feet and inner radius equal to the radius of the fountain.

2) The area of such ring is equal to the area of the outer circle less the area of the inner circle (the fountain)

Area of a circle = π × r²

Area of the outer circle: π (10ft + 5 ft)² = π (15 ft)² = 225 π ft²

Area of the inner circle = π (10ft)² = 100 π ft²

Area of the ring (sidewald) = 225π ft² - 100π ft² = 125π ft² = 392.699 ft²