# Science:Math Exam Resources/Courses/MATH110/April 2018/Question 10

MATH110 April 2018
Other MATH110 Exams

### Question 10

You decide to manufacture a can that contains a fixed volume of ${\textstyle 400cm^{3}}$ by bending a rectangular sheet of metal to form a cylinder and then soldering a circular disk at each end so that your can has both a top and a bottom.

You use a metal that cost $1 per ${\textstyle cm^{2}}$ for the side and a different metal that costs$2 per ${\textstyle cm^{2}}$ for the top and bottom. Find the radius of the can which will minimize its manufacturing cost. Show that your answer corresponds indeed to an absolute minimum.

Recall the volume of a cylinder of height ${\textstyle h}$ and base radius ${\textstyle r}$ is ${\textstyle V=\pi r^{2}h}$ and its surface area is ${\textstyle S=2\pi r^{2}+2\pi rh}$ .

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