a circular track runs around a park. there is a sidewalk that connects two points on the track that runs through the center of the park. the sidewalk is 100 ft. long. How long is the track to the nearest half foot?
The sidewalk is the diameter of the track.
Use the formula for the circumference of a circle:
C = pi * d
C = 3.14 * 100
C = ?
mmmh, isn't the sidewalk a diameter of the circle?
And isn't the the perimeter of a circle
pi(diameter) ?
To find the length of the circular track, we need to determine the circumference of the circle.
The sidewalk that connects two points on the track and runs through the center of the park represents the diameter (d) of the circle. Given that the length of the sidewalk is 100 ft, we can say that the diameter of the circle is 100 ft.
The circumference (C) of a circle is given by the formula C = πd, where π (pi) is a mathematical constant approximately equal to 3.14159.
Substituting the value of the diameter, we have C = π * 100 ft.
To find the length of the track to the nearest half foot, we need to calculate the value of C.
C ≈ 3.14159 * 100 ft ≈ 314.159 ft
Therefore, the length of the circular track to the nearest half foot is approximately 314.159 ft, which can be rounded to 314.5 ft.