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.
9. the center to the edge of a small plate measures 60 millimeters.

Explanation:

Problem 7

Step1: Identify the given measurement type

The tire's height (14 feet) is the diameter because the height of a tire (a circle) is the distance across it, which is the diameter. So, diameter \( d = 14 \) feet.

Step2: Calculate radius

Radius \( r=\frac{d}{2}=\frac{14}{2} = 7 \) feet.

Step3: Calculate circumference

Circumference \( C=\pi d=14\pi \) feet (or \( C = 2\pi r=14\pi \) feet).

Step1: Identify the given measurement type

The fence around the circular pool (76 feet long) is the circumference because it's the distance around the circle. So, circumference \( C = 76 \) feet.

Step2: Calculate diameter

Using \( C=\pi d \), we solve for \( d \): \( d=\frac{C}{\pi}=\frac{76}{\pi} \) feet (or approximately \( \frac{76}{3.14}\approx24.20 \) feet).

Step3: Calculate radius

Radius \( r=\frac{d}{2}=\frac{38}{\pi} \) feet (or approximately \( \frac{38}{3.14}\approx12.10 \) feet).

Step1: Identify the given measurement type

The distance from the center to the edge of the small plate (60 millimeters) is the radius because it's the distance from the center to the circumference. So, radius \( r = 60 \) millimeters.

Step2: Calculate diameter

Diameter \( d = 2r=2\times60 = 120 \) millimeters.

Step3: Calculate circumference

Circumference \( C = 2\pi r=120\pi \) millimeters (or \( C=\pi d = 120\pi \) millimeters, approximately 376.99 millimeters).

Answer:

• Radius: 7 feet
• Diameter: 14 feet
• Circumference: \( 14\pi \) feet (or approximately 43.98 feet)

Problem 8