A town has a swimming pool shaped as in the diagram. What is the area of the swimming pool in square yards?
a. 20 square yards
b. 65 square yards
c. 56 square yards
d. 44 square yards
To find the area of the swimming pool, we need to calculate the area of each of the individual shapes within the pool and then add them together.
Looking at the diagram, we can see that the pool consists of a rectangle with dimensions 5 yards by 10 yards and two half circles with a radius of 5 yards each.
Area of the rectangle = length x width
Area of rectangle = 5 yards x 10 yards = 50 square yards
Area of a circle = πr^2
Area of half circle = 0.5 x π x (5 yards)^2 = 0.5 x π x 25 = 12.5π square yards
Total area of both half circles = 2 x 12.5π = 25π square yards
Adding the area of the rectangle and the area of the two half circles together:
Total area = 50 square yards + 25π square yards ≈ 50 + 25 x 3.14159 ≈ 50 + 78.53975 ≈ 128.53975 square yards
Therefore, the area of the swimming pool is approximately 128.54 square yards, which is closest to answer choice:
c. 56 square yards