Question

Identify each measurement as the diameter, radius, or circumference of the circular object. Then, estimate the other two measurements for the circle.

A) For Diameter:
Radius = 10 in
Diameter = 5 in
Circumference = 62.8 in
B) For Radius:
Radius = 5 in
Diameter = 10 in
Circumference = 31.4 in
C) For Circumference:
Radius = 1.59 in
Diameter = 3.18 in
Circumference = 5 in

Answer 1

In summary, for each given circle measurement whether it's diameter, radius, or circumference, it's necessary to understand and apply the relationships between these measurements to correctly estimate the remaining dimensions of a circle using formulas like C = 2πr for circumference and A = πr² for area.

Step-by-step explanation:

When identifying measurements of a circle, it's important to understand the relationships between the diameter, radius, and circumference. The diameter of a circle is twice the radius, and the circumference is the perimeter around the circle, which can be estimated using the formula C = 2πr (where C is circumference, π is pi, and r is the radius). Let's analyze the given measurements:

• For Diameter: The correct measurements should be Radius = 5 in (as it is half of the diameter), Diameter = 10 in, and Circumference = 2π*(5 in) ≈ 31.4 in.
• For Radius: These measurements are correct. Radius = 5 in, Diameter = 10 in (2 times the radius), and Circumference = 2π*(5 in) ≈ 31.4 in.
• For Circumference: With the given Circumference = 5 in, the Radius is not correctly estimated. Using the formula C = 2πr, we would reverse calculate the radius as Radius = C / (2π) ≈ 0.795 in, and therefore the Diameter would be approximately 1.59 in.

Note that to find the area of a circle, the formula A = πr² is used, where A is the area of the circle.