anonymous
  • anonymous
The volume. V cm^3, of a cone of height h is (pi)h^3/12. If h increases at a constant rate of 0.2cm/s and the initial height is 2cm, express V in interms of t and find the rate of change of V at time t.
Mathematics
jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
So we have \[V(x)=\frac{\pi }{12} (h(x))^3\] We will let x represent the variable time for now.
myininaya
  • myininaya
Find derivative of both sides.
myininaya
  • myininaya
With respect to x

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myininaya
  • myininaya
Both V and h are functions of time this implies that both V and h are functions of x
myininaya
  • myininaya
So derivative of V is V' and derivative of h is h'
myininaya
  • myininaya
So tell me what does V' equal?

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