<p>Well this is an 2006 PSAT problem.. i think it's alright to post it. lol
Well, I got it right by plugging in numbers, but I was wondering if there was another way to solve it with out using numbers.</p>
<p>The problem goes:
The areas of the bottom, the side, and the front of a rectangular box are r,s, and t square inches, respectively. What is the volume of the box in cubic inches?
If you need the answers posted, I can..but I was wondering if there was another way of solving it.</p>
<p>bump..I'd like to know as well</p>
<p>squre root of rst</p>
<p>think about it this way
take l=length, w=width, h=height
lw=r
lh=s
wh=t
lw<em>lh</em>wh=r<em>s</em>t=l^2<em>w^2</em>h^2
how do you get rid of the squares?
square root
and u get length times width times height</p>
<p>x<em>y=r; x</em>z=s; y<em>z=t -> x</em>y<em>x</em>z<em>y</em>z=r<em>s</em>t -> x<em>y</em>z=square root r<em>s</em>t</p>
<p>Ok. Thank you you guys! I knew they had sides in common, I just couldn't think of that. I just plugged in numbers.. haha. Thank goodness that method works too.</p>
<p>akvareli - now that you know the direct approach, how about an intuitive one, based on simplicity of math?</p>
<p>You are given that formula exists.
Assume r, s, and t measured in sq.ft.
What calulations can you make with r, s, and t to get ft^3
(it's a volume measurement)?</p>
<p>The simplest one is
sqrt( sq.ft * sq.ft * sq.ft) =
sqrt (ft^6) = ft^3.</p>
<p>So sqrt(r<em>s</em>t) that is.</p>
<p>Must be one of the choices.</p>