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.
a) We know that the surface area S of a cylinder is:
S= 2*Pi*r^2+ 2*Pi*r*h ...
This looks at the relationship between surface area and volume for a cylindrical can.