The radius of a come is multiplied by 1.6 to create a radio is of a new cone with the same height. The volume of the new cone is what?

Let's call the initial radius r1 and the second radius is r2. And we know that r2=1.6 * r1.

The volume of the first cone can be calculated by V = π * r1^2 * h / 3

The volume of the second cone can be calculated by V = π * r2^2 * h / 3

If we replace r2 by using r2=1.6 * r1 then we get:

V = π * (1.6*r1) ^2 * h / 3

or V = π * 2.56 (r1) ^2 * h / 3

And so we see that the volume of the second cone is now 2.56 times bigger than the first