Connected Rate of Change involving Conical Objects
Connected Rate of Change involving Conical Objects
Water is poured into an inverted cone of radius \(6\) cm and height \(10\) cm at a rate of \(3\) cm\(^3\)/s.
- Show that the volume of the water, \(v\), in the cone at any time is given by \(v=\frac{3\pi x^3}{25}\), where \(x\) is the height of the water.
- Find the rate of change of \(x\) when the radius of the water is \(3\) cm.
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Answer:(a) \(v=\frac{3\pi x^3}{25}\) (b) \(\frac{\mathrm dx}{\mathrm dt}=\frac{1}{3\pi}\text{ cm s}^{-1}\)
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