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 2 years ago
A conical salt spreader is spreading salt at a rate of 2 cubic feet per minute. The diameter of
the base of the cone is 4 feet and the height of the cone is 5 feet. How fast is the height of the salt in the spreader
decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet?
Give your answer in feet per minute. (It will be a positive number since we use the word “decreasing”.)
 2 years ago
A conical salt spreader is spreading salt at a rate of 2 cubic feet per minute. The diameter of the base of the cone is 4 feet and the height of the cone is 5 feet. How fast is the height of the salt in the spreader decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet? Give your answer in feet per minute. (It will be a positive number since we use the word “decreasing”.)

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mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.1@AccessDenied @ash2326 @Chlorophyll @jagatuba @jhonyy9 @phi @TuringTest @Mertsj

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2always draw the pic...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1333043238193:dwthe radius of the whole cone is 2 and the height is 5

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1333043327825:dwat some given moment the cone of remaining salt is radius r and height h from this we can find similar triangles....

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1333043429599:dwso we get the proportion\[\frac25=\frac rh\implies r=\frac25h\]now we clearly need the formula for the volume of the cone, which is\[V=\frac13\pi r^2h\]to get this all in terms of one variable we will note the fact we got from the similar triangles....

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2\[V(h)=\frac13\pi(\frac25h)^2h=\frac4{75}\pi h^3\]can you differentiate this with respect to time?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2I'm trying to figure out what you did here can you just show me what you get after differentiating wrt time?

mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.12*(75)/(4)*(3.14)*(27)=.44

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2don't plug in any numbers yet

mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.1I'm using my notes. .44 is the correct answer.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2ok, I'm not using a calculator, so I didn't know that I just wanted to make sure you knew how to differentiate this with respect to time

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2I don't suppose you feel like humoring me and showing me what you get after differentiating \(before\) plugging in the numbers?

mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.1yeah... h^3 becomes 3h^2 then 3(3)^2 =27

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2no that's not how you differentiate wrt \(time\) you differentiated wrt to height, which makes this problem unsolvable

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2I mean, where did you get 0.44 aside from the fact that you already knew the answer? you forgot to differentiate \(implicitly\) h, which must be done because it is a function of time (we want rate change of height in units of time, dh/dt)

mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.1i didnt know the answer

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2so then how did you get 0.44

mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.12*(75)/(4)*(3.14)*(27)=.44 i got it by doing this ^^^^

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2ok, see I couldn't decipher that you did it right, because you plugged in the numbers already, so my brain can't read the problem backwards that fast!

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2the way I was writing... so we have\[V=\frac4{75}\pi h^3\]differentiating with respect to \(time\) we get\[{dV\over dt}=\frac4{25}\pi h^2{dh\over dt}\]so we solve for dh/dt, which you did but when you plugged in the numbers it was hard for me to see that you had done that bit correctly

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2well, nice job then :D so for future reference: these cone problems are always done using the similar triangle trick that is sort of the motto here see ya 'round

mariomintchev
 2 years ago
Best ResponseYou've already chosen the best response.1alrighty thanks :)
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