# Heating water

**Classical Mechanics**Level 4

A conical container of height \(\SI{1}{\meter}\), inner radius \(\SI{2}{\meter}\) and outer radius \(\SI{3}{\meter}\) contains water which is held at \(\SI{10}{\celsius}\). The temperature outside the container is \(\SI{80}{\celsius}\). If the thermal conductivity of the container is \(\SI{0.5}{\watt/\meter\degree\kelvin}\), find the rate of heat transfer. Give your answer in watts (\(\si{\watt}\)).

**Assumptions and Details**

- 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.