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#