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

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A 1% increase in each dimension (width, length, height) of a slab, represented by the volume formula V = xyz, results in a new volume calculated as V = (1.01x)(1.01y)(1.01z). This simplifies to V = (1.01)^3 * V_0, indicating that the volume increases by a factor of approximately 1.030301. Therefore, the overall increase in volume is about 3.03%. The discussion highlights the application of partial differential equations to understand volume changes due to dimensional increases. The calculations confirm that even small percentage increases in dimensions can lead to significant changes in volume.
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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?
 
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Re: partial differential equations

abhay said:
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: [math]V_0 = xyz[/math] (Your original volume.)

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

What is the increase in volume here?

-Dan
 
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