An open-top cylindrical container must hold 1000 cm of liquid

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

An open-top cylindrical container must hold 1000 cm

^3

of liquid. The side material costs 1 unit per cm

^2

, while the base material costs 2 units per cm

^2

. For the cheapest container, what is the ratio of height to radius,

\dfrac{h}{r}

? (a) 1 (b) \dfrac{1}{2} (c) 2 (d) 3