If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm,

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Question: If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the radius?

Options:

Correct Answer: 5.0 cm

Solution:

Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.

If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the radius?

If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the radius?

Step 1: Understand the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius.
Step 2: Identify the measured circumference from the question, which is 31.4 cm.
Step 3: Rearrange the formula to solve for the radius (r). This gives us r = C / (2π).
Step 4: Substitute the measured circumference (31.4 cm) into the formula: r = 31.4 / (2π).
Step 5: Calculate the value of r using the approximation π ≈ 3.14. So, 2π ≈ 6.28.
Step 6: Perform the division: r ≈ 31.4 / 6.28.
Step 7: Calculate the result, which gives r ≈ 5.0 cm.

Circumference and Radius Relationship – Understanding the formula for the circumference of a circle (C = 2πr) and how to derive the radius from a given circumference.
Error Propagation – Recognizing how measurement errors can affect the calculated radius and the importance of considering these errors in the final answer.