How do you find the volume of a prism if the width is x, height is #2x-1# and the length if #3x+4#?

1 Answer
Nico Ekkart
Dec 20, 2014

I'm assuming here that you mean a square prism:
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For every prism, the volume is given by the formula:
#"Volume" = "Area" times "Length"#
where #"Area"# is the area of the cross-section: the figure you would have if you were to slice a little piece off the prism.

In this case, the cross section is a rectangle. The area of a rectangle can be calculated by doing #"height" times "width"#.

So, the formula for these kind of prisms becomes:
#Volume = w*h*l#
where #w = "width", h = "height" # and # l = "length"#.

Entering your values into the formula:
#x*(2x-1)*(3x+4)#

You can bring the #x# inside the first parentheses:
#(2x^2-x)*(3x+4)#
And now, you can use FOIL.
#6x^3 + 5x^2 - 4x#

This is the volume.
I hope this is what you meant, and that it helped.

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