A can manufacturing company is designing a can of cat food to hold 5.5 oz or about 163 cm(3). They have written out that the equation for the surface area for a can with the volume is S=2pie radius(2) + 163/r. Explain why the equation is wrong and how to fix it.

The correct equation that describes the surface area is and we need to multiply by 2 in the equation described in the statement to correct the equation.

Step-by-step explanation:

Let suppose that the can of cat food is a right cylinder. The surface area of the cylinder (), measured in square centimeters, is the sum of the areas of the circular walls () and the non-circular wall (), both measured in square centimeters. That is:

(1)

By Geometry, we expanded the equation above:

(1b)

Where:

- Radius, measured in centimeters.

- Height, measured in centimeters.

And the volume of the right cylinder (), measured in cubic cnetimeters, is defined by the following formula:

Then, we clear the height of the cylinder within the volume formula:

(2)

By substituting in (1b), we obtain the following equation:

(1c)

If we know that , then the equation for the surface area of the cylinder is:

In a nutshell, we need to multiply by 2 to correct the equation.