A closed right circular cylinder must hold of liquid

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

Problem

A closed right circular cylinder must hold

500\pi\text{ cm}^3

of liquid. Manufacturing the side wall costs

0.03

dollars per

\text{cm}^2

, and each circular end costs

0.06

dollars per

\text{cm}^2

. Shipping adds an additional

0.01

dollars per

\text{cm}^2

of surface area for every part of the can. What radius

r

, in centimetres, minimizes the total cost of one can? (a)

6.3\text{ cm}

(b)

5.3\text{ cm}

(c)

4.8\text{ cm}

(d)

5.0\text{ cm}