A sculptor works with large wooden cuboids (rectangular prisms), cuts them into three smaller cuboids and then paints them black, white and grey. The volume of the black cuboid is always twice the volume of the white one and the volume of the white cuboid is always twice the volume of the grey one.
The diagram shows how this works. The cuts are always parallel to the face marked with w and h. We will always denote the surface areas of the separated cuboids by A1 (black) , A2 (white) and A3 (grey).
(see attached doc)
a) The sculptor is given a block for which l = 1, w = 6 and h = 3.
Show that with these values the ratio of A1 to A2 is 3:2
b) Show that for any cuboid the sculptor cuts, A1 is always less than 2A2
c) The sculptor wants a cuboid with h = w, which will give A1 to 3A3 . what would be the value of l in terms of w?
d) The sculptor decides she would like to have A1 to A3 = 4:3. If this is to be the case, find a formula linking l, w and h and give an example of the dimensions of a cuboid, before it is cut, for which this will work.
I need help with (d) above. Thanks.
Last edited by chugbottle; Nov 5th, 2007 at 09:04 PM.
Reason: add a line i.e. see attached doc
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