A circular grassy region with a 12 ft diameter has a 2ft by 3ft reflecting pool in its center. What is the Surface Area of the reflecting pool? What is the Area if the grass?
A = LW
A = 2 * 3
A = 6 square feet
A = pi * r^2
A = 3.14 * 6^2
A = 3.14 * 36
A = 113.04 square feet
113.04 - 6 = ______ square feet
To find the surface area of the reflecting pool, we need to calculate the area of the rectangular shape of the pool.
The formula for finding the area of a rectangle is Area = length * width.
In this case, the length of the pool is 3ft, and the width is 2ft.
Therefore, the surface area of the reflecting pool is:
Area = 3ft * 2ft = 6 square feet.
Now, to find the area of the grassy region, we need to subtract the area of the reflecting pool from the area of the circular region.
The formula for finding the area of a circle is Area = π * radius^2.
The radius of the circular grassy region is half of the diameter, which is 12ft / 2 = 6ft.
Therefore, the area of the circular grassy region is:
Area of circle = π * (6ft)^2
Area of circle = π * 36ft^2
Area of circle ≈ 113.1 square feet.
Now, we subtract the surface area of the reflecting pool from the area of the grassy region:
Area of grass = Area of circle - Surface area of pool
Area of grass = 113.1 square feet - 6 square feet
Area of grass ≈ 107.1 square feet.
So, the surface area of the reflecting pool is 6 square feet, and the area of the grassy region is approximately 107.1 square feet.