There are 3 rectangular prisms (whose length width and height are whole numbers in centimetres), whick have a surface area of 54cm2. Their lengths are 3cm, 6cm and 13cm. Find the width and height of each. Is there a formula for this.

Find the volume of each of the 3 prisms and arrange them in order from smallest to largest. What possible relationship is there between the lengths, widths and heights of your prisms and their volumes?

There are 4 rectangular prisms (whose length, width and heights are whole numbers in centimetres), which have a surface area of 78cm2. Find the length, width, height and volume of each.
Is there a formula forthis?

Desperate Ainsley

Well, surface area of a rectangular prism is twice the area of the end plus 2 times the area of one side plus 2 times the area of the third different side.

Can you work out a formula in terms of l, h and w from this?

I know the formula when you have at least one of the measurements (LBW), but is it a matter of going through hundreds of combinations to find these from just the surface area.

Not as hard as you might think, Since these are whole numbers there aren't so many combinations to try.

Here's a hint - for any lkength, width and height, the formula for surface area is
Area = 2* (LW+LH+HW) = 2*L*(W+H)+2*HW
For the case L=3: Area = 54 = 2*3*(W+H)*HW

Try some whole number conbinations for H and W. You know that both H and W must be between 1 and 9 (otherwise the right hand side would be too big) - can you get it now?