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Ainsley Ballinger · Jun 6, 2007, 01:59 AM

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

Capuchin · Jun 6, 2007, 04:35 AM

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?

Ainsley Ballinger · Jun 6, 2007, 02:37 PM

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.

ebaines · Jun 6, 2007, 06:09 PM

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?