Question

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

on the volume of the cone?
The volume of the cone is multiplied by..​

Answer 1

When the height and radius of a cone are each multiplied by 3, the volume of the cone is multiplied by 27.

Step-by-step explanation:

When the height and radius of a cone are each multiplied by 3, the effect on the volume of the cone is that the volume is multiplied by 27.

The formula for the volume of a cone is V = (1/3)πr²h. When the height and radius are multiplied by 3, the new volume would be V' = (1/3)π(3r)²(3h) = 27(1/3)πr²h = 27V.

Therefore, the volume of the cone is multiplied by 27.

Answer 2

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}=(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}=(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