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 $\gamma=2.1 \times 10^{-4}$