Volume change of a proportionally burning cylindrical candle

Volume change of a proportionally burning cylindrical candle

Junior College 1
5 marks

A solid cylindrical candle burns so that both its radius \(r\) cm and height \(h\) cm decrease over time, while remaining in the fixed proportion \(h=4r\). The total surface area of the candle, including both circular ends, is decreasing at a constant rate of \(6\pi\text{ cm}^2\text{ min}^{-1}\). Find the rate at which the volume of the candle is decreasing at the instant when \(r=3\).[5]

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Answer:\(\frac{54\pi}{5}\text{ cm}^3\text{ min}^{-1}\)

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