How Does a 1% Increase in Dimensions Affect the Volume of a Slab?

[abhay1]

Fig.(1) shows a slab whose volume V is given by
V = xyz.
If the width, the length and the height of the slab, each increases by 1%, what is the
increase in its volume?

 

[topsquark]

Re: partial differential equations

Fig.(1) shows a slab whose volume V is given by
V = xyz.
If the width, the length and the height of the slab, each increases by 1%, what is the
increase in its volume?

What figure?

I'm going guess that one corner of your slab is at the origin and everything is all nice and perpendicular.

So: \(\displaystyle V_0 = xyz\) (Your original volume.)

Now, if we add 1% to x then we have x + 0.01x = 1.01x. Similar for the other dimensions. So \(\displaystyle V = (1.01x)(1.01y)(1.01z) = (1.01)^3 xyz = (1.01)^3 V_0\)

What is the increase in volume here?

-Dan