Question

A box is formed by cutting squares from the corners of a rectangular piece of cardboard. The volume of the box is found by the equation V(h)=h(16-2h)(10-2h) where his a side of the square cutout. Which is the reasonable domain for this situation?

a. (0,5)
b. (0,10)
c. (0,8)
d. (0,infinity)

Answer 1

A. (0, 5)

Explanation:

Physically speaking, the volume of the box and the side of the square cutout are positive value. So that the following inequations must be satisfied:

`h > 0` (1)

`16-2\cdot h >0` (2)

`10-2\cdot h > 0` (3)

From (1), (2), (3) we find that:

(1):

`h > 0`

(2):

`16 > 2\cdot h`

`8 > h`

`h < 8`

(3):

`10 > 2\cdot h`

`5 > h`

`h < 5`

We see that equation above is the multiplication of a first grade monomial and two first grade binomials, which means that:

`h > 0 \,\land\,h < 5\,\land\,h< 8`

`0< h < 5`

In other words, the reasonable domain for this situation is A.