Question

Geometry help? Volume of a cone.

The volume of a cone is 1014𝜋 𝑖𝑛^3. The height of the cone is 18 𝑖𝑛.
What is the exact circumference of the base of the cone? Do NOT round at any point!

Answer 1

`"circumference "=26pi" inches"`

Explanation:

`"to find circumference we require to know the radius r"`

`"using the following formulae"`

`•color(white)(x)V_(color(red)"cone")=1/3pir^2hlarrcolor(blue)"volume of cone"`

`• " circumference (C)"=2pir`

`V_(color(red)"cone")=1/3pir^2xx18=6pir^2`

`"now volume is given as "1014pi`

`rArr6pir^2=1014pi`

`"divide both sides by "6pi`

`(cancel(6pi) r^2)/cancel(6pi)=(1014cancel(pi))/(6cancel(pi)`

`rArrr^2=1014/6=169`

`rArrr=sqrt169=13`

`rArrC=2pixx13=26pilarrcolor(red)"exact value"`

Answer 2

The volume of a cone is `V={\pir^2h}/3`

Explanation:

So, in your case:

`1014\pi={\pir^2*18}/3`

The `\pi` on each side of the equal sign will cancel, so

`1014={r^2*18}/3`

Multiply both sides by 3

`3042=r^2*18`

Then divide both sides by 18

`169=r^2`

Then, take the square root of both sides

`sqrt169=sqrtr^2`

`+-13 = r`

Since this is a distance , use the positive square root since distances can't be negative, so r = 13.

Then, the circumference of a circle is `2\pir`

So, `2*13\pi->26\pi`

That is your answer and is an exact value since it is in terms of `\pi`