If the diameter of a circle is measured as 10.0 cm with an uncertainty of 0.1 cm

₹0.0

Question: If the diameter of a circle is measured as 10.0 cm with an uncertainty of 0.1 cm, what is the circumference with uncertainty?

Options:

Correct Answer: 31.4 cm ± 0.3 cm

Solution:

Circumference = π * diameter = π * 10.0 cm ≈ 31.4 cm. Uncertainty in circumference = π * 0.1 cm ≈ 0.314 cm.

If the diameter of a circle is measured as 10.0 cm with an uncertainty of 0.1 cm, what is the circumference with uncertainty?

If the diameter of a circle is measured as 10.0 cm with an uncertainty of 0.1 cm, what is the circumference with uncertainty?

Step 1: Understand that the circumference of a circle can be calculated using the formula: Circumference = π * diameter.
Step 2: Identify the diameter given in the problem, which is 10.0 cm.
Step 3: Substitute the diameter into the formula: Circumference = π * 10.0 cm.
Step 4: Calculate the circumference using the value of π (approximately 3.14): Circumference ≈ 3.14 * 10.0 cm = 31.4 cm.
Step 5: Determine the uncertainty in the diameter, which is given as 0.1 cm.
Step 6: To find the uncertainty in the circumference, use the formula: Uncertainty in circumference = π * uncertainty in diameter.
Step 7: Substitute the uncertainty into the formula: Uncertainty in circumference = π * 0.1 cm.
Step 8: Calculate the uncertainty using the value of π: Uncertainty ≈ 3.14 * 0.1 cm = 0.314 cm.
Step 9: Combine the results to express the circumference with uncertainty: Circumference = 31.4 cm ± 0.314 cm.

Circumference Calculation – Understanding how to calculate the circumference of a circle using the formula C = π * d, where d is the diameter.
Propagation of Uncertainty – Applying the concept of uncertainty in measurements to calculate the uncertainty in derived quantities, such as circumference.