Question

if you know the circumference of a circle, which step(s) can you follow to find its diameter?

a. divide by 2.
b. divide by 2, then multiply by \\(\pi\\).
c. divide by \\(\pi\\).
d. divide by \\(\pi\\), then divide by 2.

Explanation:

Identify the circumference formula

To find the relationship between circumference and diameter, we use the standard geometric formula for the circumference of a circle.
Using the Diameter of a Circle concept, we recall:

$$C = \pi d$$

where \(C\) represents the circumference and \(d\) represents the diameter.

Solve for the diameter

To isolate the diameter \(d\) in the equation, we perform algebraic operations on both sides.
Dividing both sides of the equation \(C = \pi d\) by \(\pi\):

$$d = \frac{C}{\pi}$$

This shows that the diameter is found by dividing the circumference by \(\pi\).

Match with the given options

We compare our derived step with the multiple-choice options provided in the question.

• Option A: Divide by 2 (incorrect, this would find the radius if starting from diameter, or is unrelated).
• Option B: Divide by 2, then multiply by \(\pi\) (incorrect).
• Option C: Divide by \(\pi\) (correct, as \(d = \frac{C}{\pi}\)).
• Option D: Divide by \(\pi\), then divide by 2 (incorrect, this would find the radius).

Answer:

• (A) Divide by 2.
• (B) Divide by 2, then multiply by \(\pi\).
• (C) Divide by \(\pi\). (Correct answer)
• (D) Divide by \(\pi\), then divide by 2.