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If the Radius of a cone is tripled, the volume of the cone is how many times larger?
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.
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.
Casey W. Times the volume of the cone
2 Answers By Expert Tutors
V2=π(2r)2(3h⁄3)=12πr2(h⁄3)=12V1
Carol H. answered • 10/10/17
Experienced Mathematics Tutor w/ Master's Degree in Math
The new volume is 4 times as much as the original volume.