What is the area of a circle with a circumference of 31.4 cm? (2020)

₹0.0

Question: What is the area of a circle with a circumference of 31.4 cm? (2020)

Options:

Correct Answer: 25 cm²

Exam Year: 2020

Solution:

Circumference = 2πr; 31.4 = 2πr; r = 5 cm; Area = πr² = 25 cm².

What is the area of a circle with a circumference of 31.4 cm? (2020)

What is the area of a circle with a circumference of 31.4 cm? (2020)

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 is 31.4 cm, so we can set up the equation: 31.4 = 2πr.
Step 3: To find the radius (r), we need to isolate r in the equation. First, divide both sides by 2π: r = 31.4 / (2π).
Step 4: Calculate the value of r. Using π ≈ 3.14, we find r = 31.4 / (2 * 3.14) = 31.4 / 6.28 = 5 cm.
Step 5: Now that we have the radius, we can find the area of the circle using the formula A = πr².
Step 6: Substitute the value of r into the area formula: A = π(5 cm)².
Step 7: Calculate the area: A = π * 25 cm² = 25π cm². Using π ≈ 3.14, we find A ≈ 25 * 3.14 = 78.5 cm².
Step 8: Therefore, the area of the circle is approximately 78.5 cm².

Circumference and Area of a Circle – Understanding the relationship between the circumference and radius of a circle, and how to calculate the area using the radius.
Use of π – Recognizing the value of π in calculations and its significance in formulas related to circles.