A new race track being built is an oval that is made from a rectangle with a semi-circle on each end. If the entire track is to be fenced in, what is the minimum amount of fencing needed? (Round you=r answer to the nearest foot.): *
length= 50
width=22
Add the 50 ft lengths of the two straight sections (homestretch and backstretch)to the lengths of the two semicircular ends, which add up to the circumference of one circle of diameter D = 22 feet
Perimeter = 100 + 22 pi
To find the minimum amount of fencing needed for the race track, we need to calculate the perimeter of the entire track.
The race track is made up of a rectangle and two semi-circles.
The rectangle has a length of 50 feet and a width of 22 feet. To calculate the perimeter of the rectangle, we use the formula:
Perimeter of rectangle = 2 * (length + width)
Substituting the given values:
Perimeter of rectangle = 2 * (50 + 22) = 2 * 72 = 144 feet
Now let's calculate the perimeter of the two semi-circles at each end of the rectangle.
The semi-circles have a radius equal to half the width of the rectangle (since it forms a complete circle with the rectangle).
Radius of semi-circles = width / 2 = 22 / 2 = 11 feet
To calculate the perimeter of a semi-circle, we can use the formula:
Perimeter of semi-circle = π * radius
Since we need the total perimeter of the two semi-circles, we multiply the above result by 2:
Total perimeter of the two semi-circles = 2 * π * radius = 2 * 3.14 * 11 = 69.08 feet (rounded to the nearest hundredth)
Finally, to get the minimum amount of fencing needed, we add the perimeters of the rectangle and the two semi-circles:
Minimum amount of fencing needed = Perimeter of rectangle + Total perimeter of the two semi-circles
= 144 + 69.08 = 213.08 feet (rounded to the nearest foot)
Therefore, the minimum amount of fencing needed for the race track is approximately 213 feet.