# Heating water

**Classical Mechanics**Level 5

A conical container of height \(1\text{ m}\), inner radius \(2\text{ m}\) and outer radius \(3\text{ m}\) contains water completely filled at \({10}℃\). The temperature outside the container is \({80}^\circ C\). If the thermal conductivity of the container is \(0.5\text{ W/m-K}\), find the rate of heat transfer. Assume that the base is thermally insulated and thus no heat passes through the bottom. The conical tip of the container is cut in such a way that the inner cone's tip coincides with the upper ceiling of the container which is thermally insulated.

Give your answer in watts (\(\text{W}\)) and round your answer off to the nearest integer.

The figure below might help in imagining the container.

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