Question

A field is surrounded by racetrack it is getting sodded with new grass the race track has a rectangular center and a semi circle on each end the length of the rectangle measures 100 feet and the width measured 40 feet. how much grass is needed to cover the inside of the race track?

Answer 1

To cover the inside of the race track, you will need 82,500 square feet of grass. This can be calculated by finding the area of the rectangular center and two semi-circles on each end.

Step-by-step explanation:

To find the amount of grass needed to cover the inside of the race track, we need to calculate the area of the rectangular center and the two semi-circles on each end.

1. First, find the area of the rectangular center by multiplying its length (100 feet) by its width (40 feet): Area = 100 feet * 40 feet = 4000 square feet.
2. Next, find the area of a semi-circle by dividing its circumference by 2 and multiplying it by the radius squared. Since we know the length of the rectangle is the diameter of the semi-circle, the radius is half of that, which is 50 feet: Radius = 50 feet. The circumference of a circle can be found by multiplying its diameter by pi (approximately 3.14): Circumference = 100 feet * 3.14 = 314 feet. Therefore, the area of a semi-circle is Area = (314 feet / 2) * (50 feet * 50 feet) = 39250 square feet.
3. Since there are two semi-circles, we need to multiply the area by 2: Total Area of the Semi-circles = 39250 square feet * 2 = 78500 square feet.
4. Finally, add the area of the rectangular center and the total area of the semi-circles to find the total amount of grass needed: Total Grass Needed = 4000 square feet + 78500 square feet = 82500 square feet.