Question

A circle’s circumference is approximately 76 cm. Estimate the radius, diameter, and area of the circle. a) R= 12.10 cm, D= 24.2 cm, A= 919.45 cm² b) R= 13.5 cm, D= 27.9 cm, A= 910.66 cm² c) R= 12 cm, D= 24 cm, A= 919 cm² d) R= 14 cm, D= 27 cm, A= 910 cm²

Answer 1

Given a circle with a circumference of 76cm, the radius can be calculated as 12.1cm, the diameter as 24.2cm and the area as approximately 461cm².

Step-by-step explanation:

To determine the radius, diameter and area of a circle with a given circumference, we must rely on the formula for the circumference of a circle, which is C = 2πr (where C is the circumference and r is the radius). Given that the circumference is approximately 76 cm, we can solve for r to find the radius.

R = C/2π = 76/ 2π ≈ 12.1 cm

Determining the diameter of the circle (D) is a simple matter of doubling the radius, as the diameter is always twice as long as the radius. Hence, D= 2r = 2 * 12.1 cm = 24.2 cm.

The area of a circle (A) is given by the formula A = πr². In this case, substituting the radius we found, A = π*(12.1 cm)² ≈ 461 cm².

Therefore, option a) R= 12.10 cm, D= 24.2 cm, A= 919.45 cm² would be the closer approximation to the exact values found.

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