minatsukisaya95
  • minatsukisaya95
A small funnel in the shape of a cone is being emptied of fluid at the rate of 12 cm cube per second. The height of the funnel is 20 cm and the radius of the top is 4 cm. How fast is the fluid level dropping when the level stands 5 cm above the vertex of the cone?
Precalculus
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
let r be the radius and h be the height at any instant then r/h = 4/20 or r/h =1/5 or r=(1/5) h...
anonymous
  • anonymous
now volume at any instant is given by V=(pi)*(r^2)*h or V=(pi)*((h/5)^2)*h V=((pi)* h^3)/25 V=((pi)/25)*h^3 now differentiating wrt t both sides we have dV/dt =3*(pi/25)*h^2 *(dh/dt) now given dV/dt =-12 and h=5 ...we need (dh/dt) just solve it to get (dh/dt)
minatsukisaya95
  • minatsukisaya95
thank you i got it

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anonymous
  • anonymous
yw
goformit100
  • goformit100
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