You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of the can (radius and height) will use the least amount of material?(Hint: The lightest can will be the can with the smallest surface area.)

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

Substitute 432π for V

Divide through by π

Make h the subject:

Surface Area (A) of a cylinder is calculated as thus:

Substitute for h in

Factorize:

To minimize, we have to differentiate both sides and set

Set

Divide through by

Cross Multiply

Divide through by 2

Take cube roots of both sides

Recall that:

Hence, the dimension that requires the least amount of material is when

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rawr

im not a furry, just soft(when i want to be) <3