When DrSloth was remodeling the east wing of the Virtupets Space Station, he set aside a spherical area for the auxiliary water tankWhen full, the sphere could contain exactly 1200 cubic metres of water (or any other liquid, for that matter)However, as a cost-cutting measure, he outsourced the water tank construction to a company that only built water tanks in the shape of regular icosahedrons constructed out of 3 centimetre-thick, low-grade aluminum.If the icosahedron tank is the largest it can possibly be while still fitting within the spherical area, what is the volume of the tank in cubic metres? Please round down to the nearest tenth of a cubic metreFor example, if you find the volume to be 288.7872 cubic metres, submit 288.7 as your answer.
silicon and a doping agent usually like germanium
Try Intuitive Electronics written by a great man, the late Carl Sagen.
The radius of the sphere is easy to figure out - roughly 6.59 metersThis is also the radius of the icosahedron to the outer surfaceSince the aluminum is 3cm thick, we'll use 6.56mA sphere of radius 6.56m would have a volume of 1187.9m^3 An icosahedron inscribed in a sphere contains 60.54% of the sphere's volume 1187.9 x 0.6054 719.2 719.2 cubic meters.
