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An oil can is to be made in the form of a right circular cylinder to hold ONE QUART of oil. What dimensions of the can will require the LEAST amount of material?

The quart of oil is to be in terms of 'a', not an actual calculation of how many cubic cm a quart is

Formula: $V = (\pi)r^2h = a^3$

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  • $\begingroup$ So, what do you think the next step is? $\endgroup$ – amd Apr 18 '17 at 18:21
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HINT

How much material used is determined the by the area of the container.

Area of the bottom + area of the side

$$=\pi r^2 + 2\pi rh = \pi r^2 + \frac{2a^3}{r}$$

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