A closed cylindrical can is required to contain of liquid

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

Problem

A closed cylindrical can is required to contain

1000\text{ cm}^3

of liquid. Let

r

cm be the radius and

h

cm the height of the can. For the choice of

r

that minimizes the amount of material used, which of the following equations must be satisfied? (a)

r^{2}=\dfrac{500}{\pi}

(b)

r^{3}=\dfrac{1000}{\pi}

(c)

r^{3}=\dfrac{500}{\pi}

(d)

r^{3}=\dfrac{250}{\pi}