Answer:
A) d = [tex]\frac{C}{\pi}[/tex]
B) d = [tex]\frac{8}{\pi}[/tex] 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.
In order to solve for d, divide both sides of the equation by π:
[tex]\frac{C}{\pi} = \frac{\pi d }{\pi}[/tex]
d = [tex]\frac{C}{\pi}[/tex].
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 = [tex]\frac{C}{\pi}[/tex]
d = [tex]\frac{8}{\pi}[/tex] or 2.55 inches.
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 :
[tex]\frac{C}{2\pi } = \frac{2\pi r}{2\pi }[/tex]
r = [tex]\frac{C}{2\pi }[/tex]
Given the circumference of a circle, C = 6π:
[tex]r = \frac{6\pi }{2\pi } = 3[/tex]
Therefore, the radius of the circle is 3 inches.
