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!

2 Answers
Feb 27, 2018

"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"

Feb 27, 2018

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