# Heating water

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.
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