If volume increases by 60%, how much does the surface increase by? Please show work.

To find out how much the surface increases when the volume increases by 60%, we need to make a few assumptions:

1. The shape whose volume and surface area we are considering remains the same.
2. The dimensions of the shape scale uniformly (i.e., all dimensions increase or decrease by the same factor).

Given these assumptions, let's proceed:

1. Let's assume the initial volume is V and the initial surface area is S.
2. Since the volume increases by 60%, the final volume would be (V + 0.60V) = 1.60V.
3. To find the relationship between volume and surface area, we need to consider the formula that relates them for the specific shape being analyzed. Let's call it S = f(V). (Note: This formula can be different for different shapes.)
4. Now we can write the relationship between initial and final surface areas: S_final = f(1.60V).

Since you haven't provided the specific shape, we cannot determine the exact formula linking volume and surface area. However, you might be able to find this relationship by doing some research or referring to specific formulas for the particular shape you are interested in.

Once you have the formula relating the volume and surface area for your specific shape, you can substitute 1.60V into that formula to calculate the final surface area. The difference between the final surface area and the initial surface area will give you the increase in surface area.