# Cones are sweaty spheres

A spherical tank has a surface area of $$400\pi$$ $$m^{2}$$ and is full of water. The water is heated and its temperature rises 20 Kelvin. Due to volumetric expansion, the new volume of water now fits inside a cone whose base radius is equal to the sphere's. Find the height of that cone in meters, approximated to the nearest integer.

Details and Assumptions

1. Use $$\pi=3.14$$

2. Consider the water coefficient of volumetric expansion as $$\gamma=2.1 \times 10^{-4}$$

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