hexacordoK

2020-11-29

The formula $C=2\pi r$ the circumference C of a circle is proportional to its radius r

(a)Solve $C=2\pi r$ for r

(b) If a circle's perimeter is 15 inches, what is its radius? leave the symbol $\pi $ in your answer.

avortarF

Skilled2020-11-30Added 113 answers

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 $ the ratio of circumference to diameter is always the same.

Solution a:

$\Rightarrow C=2\pi r$

$\Rightarrow \frac{C}{\pi}=\frac{2\pi r}{pi}$ (Dividing both sides by pi)

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

$\Rightarrow \frac{C}{2\pi}=\frac{2r}{2}$ (Dividing both sides by 2)

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

$\Rightarrow r=\frac{C}{2\pi}$ (Reversing both sides)

2. Solution b: the circumference of the circle is 15 inches i,e., $C=15$ Putting the value of C in 1, we get:

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

or,$\frac{r=15}{2\pi}\text{}(C=15)$

or, $r=\frac{7.5}{\pi}$

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