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    IBMediumCalculus10–12

    Dimensions of the Cheapest 500 ml Can

    Dimensões da Lata de 500 ml Mais Barata

    A closed cylindrical can must hold 500 \text{ cm}^{3}. The cost of the metal is proportional to the total surface area. Find the radius and height that minimise the surface area, to three significant figures.

    Surface area starts with two variables, so use the fixed volume to eliminate one before differentiating. The stationary point still has to be shown to be a minimum rather than assumed.

    Solution

    Step 1 of 9

    1. 1.From the volume, h = \frac{500}{\pi r^{2}}. Surface area: