# Geometry help? Volume of a cone.

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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!

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

#### 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"#

The volume of a cone is

#### Explanation:

So, in your case:

The

Multiply both sides by 3

Then divide both sides by 18

Then, take the square root of both sides

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

So,

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