A cone with radius 2 and height 9 has its radius tripled. How many times greater is the volume of the larger cone than the smaller cone? Use pencil and paper. Explain how the volume of the cone would change if the radius were divided by three.

When increasing the radius 3 times the volume increases 9 times and when it is reduced to a third the volume decreases 9 times

Step-by-step explanation:

We have that the formula for the volume of a cone is:

Vc = pi * (r ^ 2) * h

We first calculate the original volume, where the radius is 2 and the height is 9, replacing:

Vc = 3.14 * (2 ^ 2) * 9

Vc = 113.04

Now if the radius is tripled it would be: 2 * 3 = 6, the radius would be 6, replacing:

Vc = 3.14 * (6 ^ 2) * 9

Vc = 1017.36

If we compare:

1017.36 / 113.04 = 9

This means that when the radius is tripled, the volume increases 9 times.

When if re reduces to a third the radius would be: 2/3, replacing:

Vc = 3.14 * ((2/3) ^ 2) * 9

Vc = 12.56

113.04 / 12.56 = 9

Which means that by reducing it to a third the volume becomes 9 times smaller.