# Sketching the change in a cube's volume

1. Jun 20, 2005

### wisredz

Hi all,
I've come by an interesting while studying. Here it goes

The volume $V=x^3$ of a cube of with edges of length x increases by an amount $\Delta V$ when x increases by an amount $\Delta x$. Show with a sketch how to represent $\Delta V$ geometrically as the some of the volumes of

(a) Three slabs of dimensions x by x by $\Delta x$
(b) Three bars of dimensions x by $\Delta x$ by $\Delta x$
(c) One cube of dimensions $\Delta x$ by $\Delta x$ by $\Delta x$

The differential formula $dV=3x^2*dx$ estimates the change in V with three slabs.

Well that is kinda interesting right? Why is it so? I think the rest (3 bars and a cube) is the error in the estimate. It it right?

2. Jun 20, 2005

### HallsofIvy

Staff Emeritus
Yes, that's true and I agree that it is interesting!

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