can someone help me with thisWhen 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 metre.
I got 726.48 (but of course you need to round it.) I got this because you'll find that the when an icosahedron is inscribed in a sphere, it occupies 60.54% of the sphere's volume, whatever size it isSo i took 1200 and found 60.54% of itBut then.stupid me.i forgot to take the 3cm thick casingIve guessed that to do that, you need to think about how many sides there are on a icosohedron, which is 20m and times that by 3 (the thickness) and take that away from 726.48And thats 666.48So round that up and theres your answer(I think.) Hahaha.if this is right ill be surprised cause i generally rubbish at maths:)
