Question

The area of a circle is 36π cm². What is the circumference, in centimeters? Express your answer in terms of π

Answer 1

Answer:
`12\pi`

Explanation:

The formula for area of a circle is
`\pi r^2=A`

The formula for circumference of a circle is
`2r\pi=C`

Where r is the radius

A is area

C is circumference

Knowing this we can sub our values in and solve for r in the formula for area

Divide both sides by
`\pi` to isolate r

`\pi r^2=A\\\pi r^2=36\pi \\(\pi r^2)/(\pi ) =(36\pi )/(\pi ) \\r^2=36`

Take the square root of both sides

`r^2=36\\√(r^2) =√(36) \\r=6`

Now sub the value of r into the formula for circumference

`2r\pi =C\\2(6)\pi =C\\12\pi`

Answer 2

`12\pi \: c \: m`

step by step explanation:

`area \: of \: a \: cirle = \pi \: r {}^(2) \\ circmferene \: of \: a \: circle = 2 \:\pi \: r \\ 36\pi = \pi \: r {}^(2) \\ 36 = r {}^(2) \\ r = 6 \\ for \: circmference \\ 2 * \pi \: * 6 = 12\ \: \pi \: cm`