Question

The height and radius of a cone are each multiplied by 3. What effect does this have

Answer 1

The volume of the original cone is multiplied by 27

Solution:

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:

$\text {Volume of cone}=\frac{1}{3} \pi r^{2} h$

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  

$\text {Volume of new cone}=\frac{1}{3} \pi(3 r)^{2}(3 h)=9 \pi r^{2} h$

original volume of cone x 27 = volume of new cone

Therefore, the original volume of cone is multiplied by 27