Question

1. circle a has a diameter of 3 feet. circle b has a circumference of 2 meters. which circle is bigger? explain your reasoning. (1 inch = 2.54 centimeters)

Explanation:

Step1: Convert diameter of circle A to centimeters

Since \(1\) foot \( = 12\) inches and \(1\) inch \(=2.54\) centimeters.
The diameter of circle A \(d_A = 3\) feet. First, convert feet to inches: \(3\times12 = 36\) inches.
Then convert inches to centimeters: \(36\times2.54=91.44\) centimeters.
The circumference formula is \(C=\pi d\). For circle A, \(C_A=\pi d_A\approx3.14\times91.44 = 287.1216\) centimeters.

Step2: Convert circumference of circle B to centimeters

The circumference of circle B \(C_B = 2\) meters. Since \(1\) meter \(= 100\) centimeters, \(C_B=2\times100 = 200\) centimeters.

Answer:

Circle A is bigger. Because the circumference of circle A (\(C_A\approx287.12\) centimeters) is greater than the circumference of circle B (\(C_B = 200\) centimeters).