Question

A brick wall will be shaped like a rectangular prism. The wall needs to be 3ft tall and the builders have enough bricks for the wall to have a volume of 330 cubic feet. What tool can be used to find possible dimensions for the base of the wall?

Answer 1

Answer:

For a rectangular prism that has a base area B, and a height H, the volume is:

V = B*H

This is the only "tool" that we need to use in this situation.

We know that the wall needs to be 3ft tall, then H = 3ft

And we also know that we have enough bricks for a wall of a volume:

V = 330 ft^3

If we replace these two in the volume equation, we get:

330ft^3 = B*3ft

Now we can solve this for B, and thus find the volume of the base of the wall.

To do it, we just need to divide both sides by 3ft

(330 ft^3)/3ft = B*3ft/3ft

110 ft^2 = B

This means that the area of the base is 110ft^2

As the base is a rectangle of width W and length L, we must have:

110ft^2 = B = L*W

Then the possible measures of the base are given by the linear relation:

L = 110ft^2/W

Where we also need to add some trivial restrictions, like:

L > 0 ft

W > 0ft

This only means that we can not have a length or width equal to or smaller than zero, as those do not have physical sense.