Question

problems 7–9: determine whether each measurement represents the radius, diameter, or circumference, and record it in the appropriate column of the table. then determine the exact lengths of the other two measurements of the circle.

measurement	radius	diameter	circumference
8. the fence around a circular pool is 76 feet long.

Explanation:

Step1: Analyze Problem 7

The tire's height is the diameter (since height of a tire is its diameter). So diameter \( d = 14 \) feet. Radius \( r=\frac{d}{2}=\frac{14}{2} = 7 \) feet. Circumference \( C=\pi d=14\pi\approx 43.96 \) feet.

Step2: Analyze Problem 8

The fence length is the circumference (\( C = 76 \)) feet. Diameter \( d=\frac{C}{\pi}=\frac{76}{\pi}\approx\frac{76}{3.14}\approx 24.20 \) feet. Radius \( r=\frac{d}{2}=\frac{76}{2\pi}=\frac{38}{\pi}\approx 12.10 \) feet.

Answer:

Problem 7:

• Radius: \( 7 \) feet
• Diameter: \( 14 \) feet (given as tire height)
• Circumference: \( 14\pi\approx 43.96 \) feet

Problem 8:

• Radius: \( \frac{38}{\pi}\approx 12.10 \) feet
• Diameter: \( \frac{76}{\pi}\approx 24.20 \) feet
• Circumference: \( 76 \) feet (given as fence length)