Question

An open box is made by cutting squares from the corners of a piece of

metal that is 16 inches by
20 inches, as shown in the figure. The edge of each cut-out square is x inches. Find V(x), the
volume of the box in terms of x.

Answer 1

The volume of the box is

V(x) = 4x^3 -72x^2+320x

Explanation:

Here, we are interested in calculating the volume of the box

From what we can see, the shape of the box is a cuboid

Mathematically, the volume of a cuboid is l * b * h

Thus, what we have will be;

x * 20-2x * 16-2x

= x ( 20(16-2x) -2x(16-2x))

= x(320-40x-32x + 4x ^2)

= x(320-72x+4x^2)

= 320x-72x^2 + 4x^3

the volume v(x) will be;

V(x) = 4x^3 -72x^2+320x