Question

1. the circumference of a circle is 18π in. find its diameter, in inches.
2. the circumference of a circle is 10π cm. find its radius, in centimeters.
3. the radius of a circle is 10 in. find its circumference in terms of π.

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = \pi d$ (where $C$ is the circumference and $d$ is the diameter) or $C = 2\pi r$ (where $r$ is the radius).

Question 1

Step1: Apply the formula $C=\pi d$

Given $C = 18\pi$ in. Substitute into $C=\pi d$. We get $18\pi=\pi d$.

Step2: Solve for $d$

Divide both sides of the equation $18\pi=\pi d$ by $\pi$. So $d = 18$ in.

Question 2

Step1: Apply the formula $C = 2\pi r$

Given $C=10\pi$ cm. Substitute into $C = 2\pi r$, we have $10\pi=2\pi r$.

Step2: Solve for $r$

Divide both sides of the equation $10\pi = 2\pi r$ by $2\pi$. So $r = 5$ cm.

Question 3

Step1: Apply the formula $C = 2\pi r$

Given $r = 10$ in. Substitute into $C=2\pi r$. Then $C=2\pi\times10=20\pi$ in.

Answer:

1. 18 in
2. 5 cm
3. $20\pi$ in