The volume of the original cone is multiplied by 27
We have been given that the height and radius of a cone are each multiplied by 3.
We need to find what effect it has on the volume of the cone.
The volume of the original cone is given as follows:
[tex]\text {Volume of cone}=\frac{1}{3} \pi r^{2} h[/tex]
Now, the radius and height are multiplied by 3.
Therefore, the new radius is ‘3r’ and the new height is ‘3h’.
Hence the new volume is
[tex]\text {Volume of new cone}=\frac{1}{3} \pi(3 r)^{2}(3 h)=9 \pi r^{2} h[/tex]
original volume of cone x 27 = volume of new cone
Therefore, the original volume of cone is multiplied by 27
