(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rectangular prism has its length increasing by 12 cm/min, its width increasing by 4 cm/min and its height increasing by 2 cm/min. How fast is it's volume changing when the dimensions are 200 cm in length, 50 cm in width and 30 cm in height?

2. Relevant equations

3. The attempt at a solution

I am reworking a few things for an online calculus course that I am about to finish. This questions seems to have me baffled though. I have worked out the equations to arrive at dv/dt, however when I try to complete ( by attempting to arrive at (t) or use the quadratic equations the values I arrive at are always negative?

Here we go,

dL/dt= 12cm/min dW/dt=4cm/min dH/dt=3cm/min

How fast is the change occuring when∶ L=200 W=50 H=30

V=LWH

V=(200+12t)(50+4t)(30+3t)

dv/dt=10,000+800t+600t+48t^2 (30+3t)

=300000+20000t+24000t+1600t+18000t+1200t^2+1440t^2+96t^3

= 96t^3+ 2648t^2+63600t+300000

=2〖(96t)〗^2+2(2648t)+63600

=192t^2+5296t+63600

∴at t=2cm/min

This is where I get lost, I have tried using v(t)=x(t)y(t)z(t) and keep running into (-) values.Hopefully someone can shed a little light on this one for me.

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# Homework Help: Related Rates (rectangular prism)

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