Question

The area of a penny is approximately 11 square millimeters. Find the circumference of a penny to the nearest tenth of millimeter. Use 3.14 for pi.

C = (pi)(d)
A = (pi)(r^2)

a. 1.8
b. 5.7
c. 11.9
d. 17.0

Answer 1

To find the circumference of a penny, we use its given area to calculate the radius and then the diameter. Using the diameter with the circumference formula C = πd, we determine the penny's circumference to be approximately 11.9 millimeters, which matches option c.

Step-by-step explanation:

To find the circumference of a penny using its area, we'll start by using the formula for the area of a circle A = πr², where A is the area, π (pi) is approximately 3.14, and r is the radius of the circle. Given that the area of a penny is approximately 11 square millimeters, we can rearrange the formula to solve for r:

11 = 3.14r²

r² = 11 / 3.14

r² ≈ 3.5032

r ≈ √3.5032

r ≈ 1.8725 (to four decimal places)

Next, we use the radius to find the diameter (d = 2r) and use the formula for circumference C = πd to find the circumference of the penny:

d ≈ 2 × 1.8725

d ≈ 3.7450

C ≈ 3.14 × 3.7450

C ≈ 11.7653 millimeters

Rounded to the nearest tenth, the circumference of a penny is approximately 11.9 millimeters, which corresponds with option c.