Question

2. A box with a square base and no top is to be constructed so that it has a volume
of 1000 cubic centimeters. Let x denote the width of the box, in centimeters. Express
the height h in centimeters as a function of the width x (Hint: use the volume
formula).​

Answer 1

Given:

Width of box = x cm

Height of the box = h cm

Volume of box = 1000 cubic centimeters

Let:

Length of box be l cm

To find:

h as function of x

Solution:

Volume of box =

$h \times x \times l$

h. x. l= 1000

But since given that base of box is square

so, x=l

substituting,

$h {x}^{2} = 1000$

or

$h = \frac{1000}{ {x}^{2} }$

Hence, height of box is 1000/x^2 cm.