Solve the following problem: A town has a swimming pool shaped as in the diagram.
What is the area of the swimming pool in square yards?
(1 point)
• 30 square yards
• 56 square yards
• 44 square yards
• 65 square yards
To find the area of the swimming pool, we need to calculate the area of the rectangle and the area of the two semi-circles.
1. The rectangle:
The length of the rectangle is 8 yards and the width is 5 yards.
Area of rectangle = length * width
Area of rectangle = 8 yards * 5 yards
Area of rectangle = 40 square yards
2. The two semi-circles:
The diameter of the semi-circle is the same as the width of the rectangle, which is 5 yards.
Radius of the semi-circle = Diameter / 2
Radius = 5 yards / 2 = 2.5 yards
Area of one semi-circle = π*r²/2
Area of one semi-circle = π*2.5²/2
Area of one semi-circle = π*6.25/2
Area of one semi-circle = 3.125π square yards
Area of two semi-circles = 2 * 3.125π
Area of two semi-circles = 6.25π square yards
Total area of swimming pool = Area of rectangle + Area of two semi-circles
Total area = 40 square yards + 6.25π square yards
Total area ≈ 40 square yards + 19.63 square yards
Total area ≈ 59.63 square yards
Therefore, the area of the swimming pool is approximately 59.63 square yards, which is closest to 56 square yards.