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finalaeon123

  • 2 years ago

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.

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  1. myininaya
    • 2 years ago
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    So we have \[V(x)=\frac{\pi }{12} (h(x))^3\] We will let x represent the variable time for now.

  2. myininaya
    • 2 years ago
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    Find derivative of both sides.

  3. myininaya
    • 2 years ago
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    With respect to x

  4. myininaya
    • 2 years ago
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    Both V and h are functions of time this implies that both V and h are functions of x

  5. myininaya
    • 2 years ago
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    So derivative of V is V' and derivative of h is h'

  6. myininaya
    • 2 years ago
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    So tell me what does V' equal?

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