 # The formula C=2pi r relates the circumference C of a circle to its radius r. (a)Solve C=2pi r for r (b) If a circle's circumference is 15 inches, what is its radius? leave the symbol pi in your answer. hexacordoK 2020-11-29 Answered
The formula $C=2\pi r$ relates the circumference C of a circle to its radius r.
(a)Solve $C=2\pi r$ for r
(b) If a circle's circumference is 15 inches, what is its radius? leave the symbol $\pi$ in your answer.
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1. The given formula is $C=2\pi r$ where, C is the circumference of a circle. r is radius of a circle. and, $\pi$ is the constant ratio of circumference to diameter.
Solution a:
$⇒C=2\pi r$
$⇒\frac{C}{\pi }=\frac{2\pi r}{pi}$\ (Dividing both sides by pi)
$⇒\frac{C}{\pi }=2r$
$⇒\frac{C}{2\pi }=\frac{2r}{2}$\ (Dividing both sides by 2)
$⇒\frac{C}{2\pi }=r$
$⇒r=\frac{C}{2\pi }$\ (Reversing both sides)
2. Solution b: Circumference of circle = 15 inches i,e., $C=15$ Putting the value of C in 1, we get:
$r=\frac{C}{2\pi }$
or,
or, $r=\frac{7.5}{\pi }$