Question

The formula for the circumference of a circle with diameter d is C = πd.

Answer 1

Answer:

A) d = $\frac{C}{\pi}$

B) d = $\frac{8}{\pi}$ or 2.55 inches

C) r = 3 inches

Step-by-step explanation:

Given the formula for the circumference of a circle, C = πd, where d represents the diameter of a circle.

A. solve the formula for d.

In order to solve for d, divide both sides of the equation by π:

$\frac{C}{\pi} = \frac{\pi d }{\pi}$

d = $\frac{C}{\pi}$.

B. The circumference of a circle is 8 inches. What is the diameter of the circle?

Given the circumference of the circle, C = 8 inches:

Use the formula for the diameter of the circle from part A of this post.

d = $\frac{C}{\pi}$

d = $\frac{8}{\pi}$ or 2.55 inches.

C. The circumference of the circle is 6π inches. what is the radius of the circle.

Since the diameter of a circle is the same as twice the measure of the radius, r:  d = 2 × r

Then, we can rewrite the formula for the circumference of a circle as:

C = 2πr

Divide both sides by 2π to isolate r :

$\frac{C}{2\pi } = \frac{2\pi r}{2\pi }$

r = $\frac{C}{2\pi }$

Given the circumference of a circle, C = 6π:

$r = \frac{6\pi }{2\pi } = 3$

Therefore, the radius of the circle is 3 inches.