An open-top box with a square base is to be made from material that provides a total…

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

Problem

An open-top box with a square base is to be made from material that provides a total surface area of

192\text{ cm}^2

(including the base but not a lid). Let

x

be the length of a side of the base and

h

the height. What is the height of the box that maximizes its volume? (a)

6\text{ cm}

(b)

4\text{ cm}

(c)

2\text{ cm}

(d)

8\text{ cm}