Question

identify each measurement as the diameter, radius, or circumference of the circular object. then, estimate the other two measurements for the circle.
a. the length of the minute hand on a clock is 5 inches.
b. the fence around a circular pool is 75 feet long.
c. the tires on a mining truck are 14 feet tall.

Explanation:

Step1: Identify the measurement type for part a

The minute - hand of a clock is like the radius of a circle. If \(r = 5\) inches.
Using the formula \(d=2r\), we get \(d = 2\times5=10\) inches.
Using the formula \(C = 2\pi r\approx2\times3.14\times5 = 31.4\) inches.

Step2: Identify the measurement type for part b

The fence around a circular pool is the circumference. If \(C = 75\) feet.
Using the formula \(C=\pi d\), then \(d=\frac{C}{\pi}\approx\frac{75}{3.14}\approx24\) feet.
And \(r=\frac{d}{2}\approx\frac{24}{2}=12\) feet.

Step3: Identify the measurement type for part c

The height of the tire (from the ground to the top of the tire) is the diameter. If \(d = 14\) feet.
Using the formula \(r=\frac{d}{2}=\frac{14}{2}=7\) feet.
Using the formula \(C=\pi d\approx3.14\times14 = 43.96\) feet.

Answer:

a. The length of the minute - hand is the radius. The diameter is \(10\) inches and the circumference is approximately \(31.4\) inches.
b. The fence length is the circumference. The diameter is approximately \(24\) feet and the radius is approximately \(12\) feet.
c. The tire height is the diameter. The radius is \(7\) feet and the circumference is approximately \(43.96\) feet.