# Thread: Question on bounds - volume of pyramid

1. ## Question on bounds - volume of pyramid

Hi I have a question which asks for an expression for the difference between the upper and lower bounds of a square based pyramid's volume. The length of the base's side is x metres, whilst the vertical height is y metres.

I know that the upper bound(and lb) equation would be for the volume:
1/3(x+1/2)^2(y+1/2)
(for the lb you would replace the + symbol with - symbols)

However the part I'm struggling on is symplifying the expression I got down:

difference = 1/3(x+1/2)^2(y+1/2) - 1/3(x-1/2)^2(y-1/2)

Would it require me to expand the brackets then factorise? (although that seems strangely long for a 3 mark question)

Would it involve moving parts of the equation across the equal sign?

or is it incredibly simple and I'm just missing something badly...

Thanks, any help would be greatly appreciated.

2. Hello, David!

Your reasoning and work are correct . . .

[Difference .= .(1/3) [(x + ½)²(y + ½) - (x - ½)²(y - ½)]
I'd say that you've satisfied the problem.
. . You've found "an expression for the difference between ..."

Any additional simplifying would be superfluous work . . . IMHO.

3. Thanks for the reply; I also checked the answer with others, it seems to be correct as it is

### Square based pyramid volume calculate the upper and lower bound

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