A circle has a circumference of 31.4 cm. What is the radius of the circle?

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Question: A circle has a circumference of 31.4 cm. What is the radius of the circle?

Options:

Correct Answer: 5 cm

Solution:

Circumference = 2πr => 31.4 = 2πr => r = 31.4/(2π) = 5 cm.

A circle has a circumference of 31.4 cm. What is the radius of the circle?

A circle has a circumference of 31.4 cm. What is the radius of the circle?

Step 1: Understand that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
Step 2: We know the circumference (C) is 31.4 cm. So we can write the equation: 31.4 = 2πr.
Step 3: To find the radius (r), we need to isolate r in the equation. First, divide both sides of the equation by 2π: r = 31.4 / (2π).
Step 4: Now, calculate the value of r. Use the approximate value of π (3.14) for easier calculation: r = 31.4 / (2 * 3.14).
Step 5: Calculate 2 * 3.14, which equals 6.28. Now divide 31.4 by 6.28: r = 31.4 / 6.28.
Step 6: Perform the division: r = 5 cm. This is the radius of the circle.

Circumference of a Circle – The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius.
Solving for Radius – To find the radius from the circumference, rearranging the formula to r = C/(2π) is necessary.