anonymous
  • anonymous
Sand is falling on a pile , having shape pf a cone, at the rate 1.5 m3/min. assime diameter of base is 3 times the altitiude, at what rate is the altitude increasing when the altitude is 2m?
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@ganeshie8 @ParthKohli @Loser66
anonymous
  • anonymous
whats is "r" equal too ?
anonymous
  • anonymous
the question says 3d=h

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anonymous
  • anonymous
radius is half so 2/3r=h?
anonymous
  • anonymous
other way around. d = 3h
anonymous
  • anonymous
so r = 3h/2
anonymous
  • anonymous
and V = πr²h/3, so make the substitution for r then take the derivative
anonymous
  • anonymous
okey i did eberyhing i am getting 1/9pi and u ?
anonymous
  • anonymous
i did somthing wrong
anonymous
  • anonymous
yeah I got something different? What was your derivative?
anonymous
  • anonymous
did u get 1/6pi?
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
If you mean \[\Large \frac{1}{6\pi}\] then you are correct
anonymous
  • anonymous
how ?
anonymous
  • anonymous
oh, that's what I thought you meant
jim_thompson5910
  • jim_thompson5910
what did you get for dV/dt ?
anonymous
  • anonymous
my der was 9/12pih3 dh/dt?
anonymous
  • anonymous
after putiing in 3/2h
jim_thompson5910
  • jim_thompson5910
the h^3 part is incorrect
anonymous
  • anonymous
how
jim_thompson5910
  • jim_thompson5910
you will have h^3 in the V volume formula but after you derive, it turns into 3h^2
anonymous
  • anonymous
the formula for cone is x=1/3r2h
anonymous
  • anonymous
when 3/2h goes in it become h2 then h3 by timising the outside h
anonymous
  • anonymous
|dw:1433903048615:dw|
anonymous
  • anonymous
|dw:1433903137752:dw|
anonymous
  • anonymous
ok what are the steps take the derv fist then sub?
anonymous
  • anonymous
Sub for r first because we don't have a value for dr/dt, then take the derivative
anonymous
  • anonymous
wait so (3h/2) doesnt equal 9h2/4? it eiqls 9h/4?
anonymous
  • anonymous
oh wait i think i get it now
anonymous
  • anonymous
you good?
anonymous
  • anonymous
h is 2 right
anonymous
  • anonymous
yes
anonymous
  • anonymous
then 9(2)^2 = 36
anonymous
  • anonymous
hold on the 1/3 is gone beacuse of derv right
anonymous
  • anonymous
well the 1/3 was gone before the derivative. It was 3/4 after the substitution, and 9/4 after the derivative
anonymous
  • anonymous
damn i am going to take 5 min brake
dumbcow
  • dumbcow
\[V = \frac{1}{3} \pi r^2 h\] \[r = \frac{3}{2} h\] \[\rightarrow V = \frac{1}{3} \pi (\frac{3}{2}h)^2 h = \frac{3}{4} \pi h^3\] Take derivative with respect to time \[\frac{dV}{dt}= \frac{9}{4} \pi h^2 \frac{dh}{dt}\] plug in dV = 1.5, h =2 , then solve for dh/dt \[\frac{dh}{dt} = \frac{1.5}{9 \pi}\]

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