A designer of vegetable cans wants to redesign the cans by enlarging the area of the base to twice the original size. The new can should hold the same amount of vegetables. How should the designer change the height of the can?

The answer to the question is below:

If the designer of vegetable cans wants to double the area of the base of his new can but keep the same amount of content (i. e. the same volume), what he should do with height is to reduce it by half.

Explanation:

We will perform the appropriate mathematical process so you can see the change in the design of the can:

1. Suppose the can is cylindrical, since the vast majority of cans are, the volume formula that applies to a cylinder is:

V = π*r^2*h

Where:

r = base radius

h = height.

You should keep in mind that the area of the base is equal to:

A = π*r^2

Therefore the volume formula could be:

V = A*h

We will provide a value of the volume (or the amount of product contained in the can) which will be 100 cm^3 in international units. If at the same time we assume that the area of the cylinder base is 12.5 cm^2, the formula would be:

100cm^3 = 12.5cm^2 * h

Height is cleared to calculate:

h = 100cm^3 / 12.5cm^2 h = 8 cm

Now if we double the area (that is 25 cm^2) but the volume is maintained, we have:

h = 100cm^3 / 25cm^2 h = 4 cm

In the two different height values you can identify that by doubling the area, the height was reduced by half.