Question

the diagram below shows a top - view of the paths of two rides at a carnival.

• path a is a circle with radius 14 feet.
• path b is a circle with radius 35 feet.

how much longer is the circumference of path b than path a?
leave your answer in terms of \\(\pi\\). (\\(c = 2\pi r\\))

Explanation:

Step1: Recall Circumference Formula

The formula for the circumference of a circle is \( C = 2\pi r \), where \( r \) is the radius of the circle.

Step2: Calculate Circumference of Path A

For Path A, the radius \( r_A = 14 \) feet. Substitute into the formula:
\( C_A = 2\pi(14) = 28\pi \) feet.

Step3: Calculate Circumference of Path B

For Path B, the radius \( r_B = 35 \) feet. Substitute into the formula:
\( C_B = 2\pi(35) = 70\pi \) feet.

Step4: Find the Difference

Subtract the circumference of Path A from Path B:
\( C_B - C_A = 70\pi - 28\pi = 42\pi \) feet. If we use \( \pi=\frac{22}{7} \), then \( 42\times\frac{22}{7}= 132 \) feet.

Answer:

The circumference of Path B is \( 42\pi \) (or 132) feet longer than Path A.