# Cones are sweaty spheres

**Classical Mechanics**Level 3

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*

Use \(\pi=3.14\)

Consider the water coefficient of volumetric expansion as \(\gamma=2.1 \times 10^{-4}\)