Surface Area of a can is 517.8 cm^2. Maximize the volume of this can using the measured surface area.

--- Radius

--- Height

Explanation:

Given

Object: Can (Cylinder)

Required

Maximize the volume

The surface area is:

Substitute 517.8 for S.A

Divide through by 2

Factorize:

Divide through by

Make h the subject

--- (1)

Volume (V) is calculated as:

Substitute (1) for h

Open Bracket

Differentiate V

Set V' to 0

Collect Like Terms

Divide through by 3

Divide through by

Take square root of both sides

Recall that:

Substitute 5.24 for r

Hence, the dimension that maximize the volume is:

--- Radius

--- Height

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