# Surface area and volume

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Solve the following word problem, you will need to know that a cylinder of radius r and height h has volume V = Pi r^2 h. Also, a circle of radius r has area A = Pi r^2 and circumference C = 2 Pi r.

A closed cylindrical can has a radius t and height h.

a) If the surface area S of the can is a constant, express the volume V of the can in terms of S and r.

b) If the volume V of the can is a constant, express the surface area S in terms of V and r.

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##### Solution Summary

This looks at the relationship between surface area and volume for a cylindrical can.

##### Solution Preview

a) We know that the surface area S of a cylinder is:

S= 2*Pi*r^2+ 2*Pi*r*h ...

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