Posted by Joel on October 30, 2002 at 01:00:52:
In Reply to: Related Rates Problems posted by C. Slayden on October 29, 2002 at 18:06:30:
: 3.All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is 1 centimeter?
: My work. Took the volume for a cube and differentiated it dv/dt=dl/dt(dw/tw)(dh/dt) and just plugged in the 1 for each and recieved a answer of 1. I have no clue if I did that right.
If you thought your answers to #2 (which were correct) were "hilatious", what did you think about this one? C'mon. If each edge is increasing at the rate of 3 cm/sec, how could the volume be increasing by only 1 cc/sec?
Anyway, this problem is almost the same as #2 and you had the method exactly right for that one. There it was dv/dt = dv/dr * dr/dt where r was the radius.
The volume of a cube is just
v = s^3 where s is a side.
so now use dv/dt = dv/ds * ds/dt
Try it again. (You should get 9 cc/sec.)
Incidentally, when you work on problems involving purely abstract equations you can ignore units. But when you have problems like these, involving measurements of actual objects and time, don't give the answer as just plain "9". It's 9 SOMETHINGS, and you have to pay attention to what those SOMETHINGS are, because otherwise you'll get screwed on a test when they switch units on you (for example giving a distance measurement in inches and a speed in feet/second, or giving a speed in miles per hour and a distance in feet and asking where something is after 2 minutes, etc).
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