Question

find the circumference of each circle.

1. area = 64π mi²

16π mi

1. area = 16π in²

8π in
find the area of each.

1. circumference = 6π yd

9π yd²

1. circumference = 22π in

121π in²
critical thinking question:

1. find the radius of a circle so that its area and circumference have the same value.

r = 2

Explanation:

Step1: Recall circle - area and circumference formulas

The area formula of a circle is $A = \pi r^{2}$, and the circumference formula is $C=2\pi r$.

Step2: Set area equal to circumference

Set $\pi r^{2}=2\pi r$.

Step3: Solve the equation

First, subtract $2\pi r$ from both sides to get $\pi r^{2}-2\pi r = 0$. Factor out $\pi r$: $\pi r(r - 2)=0$. Then, we have two solutions for $r$ from the zero - product property. $\pi r=0$ gives $r = 0$ (but a circle with radius $r = 0$ is a degenerate case and not a real - world circle), and $r-2=0$ gives $r = 2$.

Answer:

$r = 2$