A can manufacturing company is designing a can of cat food to hold 5.5 oz, or about 163 cm3. They have written out that the equation for the surface area for a can with this volume is S=2πr2+163r. Explain why the equation is wrong and how to fix it.

S = 2πr + 326/r

Step-by-step explanation:

Given

Volume = 163cm³

Required

Explain why S = 2πr² + 163r is not correct

The volume (V) of a cylinder is:

V = πr²h (1)

And the surface area (S) is:

S = 2πr² + 2πrh (2)

Make h the subject in (1)

h = V/πr²

Substitute V/πr² for h in (2)

S = 2πr² + 2πr(V/πr²)

Simplify the express in bracket

S = 2πr² + (2πrV)/(πr²)

S = 2πr² + 2V/r

Substitute 163 for V

S = 2πr + 2 * 163/r

S = 2πr + 326/r

The above shows the correct equation that solves the surface area and also shows how it was fixed by substituting proper values and following due process.