Question

Suppose the area of a ˚le is approximately 113 square cm. What is the ˚umference of the ˚le? Use 3.14 for π. Round to the nearest thousandth.

a) 11.959 cm
b) 12.567 cm
c) 13.453 cm
d) 14.265 cm

Answer 1

To find the circumference of a circle with an area of approximately 113 square centimeters, use the formula A = πr² to solve for the radius, then use C = 2πr to find the circumference. The calculations suggest a circumference of approximately 37.68 cm, which does not match the provided options.

Step-by-step explanation:

To find the circumference of a circle when given the area, you can use the relationship between the area and the radius, and then find the circumference using the radius. The area of a circle (A) is given by πr², and the circumference (C) is given by 2πr. If we know the area is approximately 113 square centimeters, we first solve for the radius using the area formula:

A = πr².

Substituting 113 for A and 3.14 for π, we get:

113 = 3.14r²

Next, we solve for r²:

r² = 113 / 3.14

r² ≈ 36

Then, we take the square root to find r:

r ≈ 6 cm.

Now, we use the radius to find the circumference:

C = 2πr

C ≈ 2 × 3.14 × 6

C ≈ 37.68 cm.

Since the options given do not match this result, it appears there is a mistake in either the calculation or the options provided. We should revisit the calculations or verify the options with additional sources.