If cone radius tripled, how many times larger is volume?

[DestinyLazaro]

If the Radius of a cone is tripled, the volume of the cone is how many times larger?

 

[soroban]

Re: Radius? Volume? HELP!!!

Hello, DestinyLazaro!

If the radius of a cone is tripled, the volume of the cone is how many times larger?

$\displaystyle \text{The volume of the original cone is: }\:V_1 \;=\;\tfrac{1}{3}\pi r^2h$

$\displaystyle \text{If the radius is tripled to }3r\text{, then: }\:V_2 \:=\:\tfrac{1}{3}\pi (3r)^2h \:=\:3\pi r^2h$

$\displaystyle \text{We have: }\:\frac{V_2}{V_1} \:=\:\frac{3\pi r^2h}{\frac{1}{3}\pi r^2h} \:=\:9$

Therefore, the new cone is 9 times larger.

 

[fasteddie65]

Re: Radius? Volume? HELP!!!

Remember that the ratio of the volumes is the cube of the scale factor, i.e. the ratio of two corresponding lengths.