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Volume maximization explained with an example

Find the dimensions of a cylinder with a surface area of 300 cm^2 with a maximum volume.

Solution Preview

The surface area of the cylinder is,

300 = 2(pi r^2) + (2pi rh)......(1)

and the cylinder is, V = (pi) r^2 h .....(2)

where h is the height of the cylinder and r its radius.

To find the maximum volume we ...

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