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Minimise metal for a cylinder with a hemispherical cap

A closed thin-metal container is a cylinder with a hemispherical cap at one end. Find the minimum area of metal required for a volume of 100 cm3100\text{ cm}^3. Given sphere volume 43πr3\frac43\pi r^3 and surface area 4πr24\pi r^2.

CJC · Lecture · Example 14

Draw and label the variables, use the constraint to reduce to one variable, then differentiate.

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