Math 30 Project ? please help?

Sep 17, 2008 | candle kits

you have decided to start a part time job selling candle kits.each kit will contain 25 cubic inches of wax and a mold for making a pyramid shaped candle with a square base. you would like the hight to be 2 inches less then the length of each side of the candles square base. determine the dimensions of the mold that will achieve this shape?
a)let X represent the length of each side of the base and H represent the hight ?
b)find the formula for the volume of the square based pyramid and write the volume as a polynomial function of X
c)sketch the volume to 25 and solve for X.
show all the steps in your solution please ! im not asking you to solve the whole problem im not sure where to start so any help is very appreciated
i think i need to use this formula for B.
V(x)= X^2+H/3

The volume of any pyramid is one third the area of the base times the height.

So, for your square-based candle, you have:
V = H.X^2 / 3

But, you know that H = X - 2, so:
V = (X-2).X^2 / 3
Expand :
V = 1/3.X^3 - 2/3.X^2

Sketch and solve.
You might find it easier to find when 3V is 75 instead:
3V = x^3 - 2.x^2

You should find that V=25 (or 3V=75) when X is 5.

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One Response to “Math 30 Project ? please help?”

  1. Pete Says:
    February 21st, 2008 at 9:07 pm

    The volume of any pyramid is one third the area of the base times the height.

    So, for your square-based candle, you have:
    V = H.X^2 / 3

    But, you know that H = X - 2, so:
    V = (X-2).X^2 / 3
    Expand :
    V = 1/3.X^3 - 2/3.X^2

    Sketch and solve.
    You might find it easier to find when 3V is 75 instead:
    3V = x^3 - 2.x^2

    You should find that V=25 (or 3V=75) when X is 5.
    References :

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