Question

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.

Answer 1

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

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.