Question

A cylindrical can has a volume of 2in^(3). Express the surface area of the can as a function of its radius,r.

Answer 1

$V=2 \text{ in}^3\\ A=2\pi r (r+h)\\ h=?\\\\ V=\pi r^2h=2\\ \pi r^2h=2\\ h=\dfrac{2}{\pi r^2}\\ A=2\pi r\left(r+\dfrac{2}{\pi r^2}\right)\\ \boxed{A=2\pi r^2+\dfrac{4}{r}}$