Question

circle a has a diameter of 1 foot. circle b has a circumference of 1 meter. which circle is bigger? explain your reasoning. (1 inch = 2.54 centimeters)

Explanation:

Step1: Convert the diameter of Circle A to centimeters

Since 1 foot = 12 inches and 1 inch = 2.54 centimeters, then the diameter of Circle A \(d_A=12\times2.54 = 30.48\) centimeters.
Using the formula for the circumference of a circle \(C=\pi d\) (where \(C\) is the circumference and \(d\) is the diameter), the circumference of Circle A is \(C_A=\pi\times30.48\approx3.14\times30.48 = 95.77\) centimeters.

Step2: Convert the circumference of Circle B to centimeters

Since 1 meter = 100 centimeters, the circumference of Circle B \(C_B = 100\) centimeters.

Answer:

Circle B is bigger. Because the circumference of Circle A is approximately \(95.77\) centimeters and the circumference of Circle B is \(100\) centimeters, and \(100>95.77\).