Question

A circular piece of wood had a circumference of exactly 60.5 inches. Which measurement is closest to the radius, in inches, of the piece of wood? Use 3.14 as an approximation of π.

Answer 1

To find the radius of a circle with a known circumference of 60.5 inches, we can apply the formula C = 2πr and solve for the radius (r) by dividing the circumference by 2π (where π is approximated as 3.14). The calculated radius is approximately 9.64 inches.

Step-by-step explanation:

The student is asking about the relationship between the circumference of a circle and its radius. The standard formula for the circumference (C) of a circle is C = 2πr, where π (pi) is approximately 3.14 and r is the radius of the circle. Given that the circumference is 60.5 inches, we can use the formula to find the radius.

First, we substitute the given values into the formula:

C = 2πr

60.5 = 2 × 3.14 × r

To solve for r, divide both sides by 2π:

r = 60.5 / (2 × 3.14)

r ≈ 60.5 / 6.28

r ≈ 9.64 inches

Thus, the radius of the piece of wood is approximately 9.64 inches.