@eversoclever,
Quote:As with a number of these problems there is a missing piece of information, and a bit of ambiguity in the question.
Firstly, we do not know the thickness of the sphere Dr. Sloth intended to be built. As the spherical area set aside had to contain the sphere and it's contents, the area would have to have been greater than that calculated from 1200 cubic metres (unless he was using advanced Virtupets materials which allowed such volumes to be contained using a thickness of 0.0(lots more zeros)1) metres.
Secondly, the question asks for the volume of the tank, but is unclear as to whether this is the volume of the tank including or excluding its contents.
Okay, to attempt to answer your question, I'll try to provide my reasoning.
First, the question says Sloth set aside a spherical
area, not an area for a spherical tank that could contain a volume of water. The actual area he left available was able to contain the 1200 cubic metres of water. So, there is no thickness because we are not considering any tank in that area.
Second, when asked for the volume of a tank of water, say the water that we buy for our watercoolers, our being those of us that have one, we use the volume of liquid that is contained inside. Or, for another example, with gasoline containers, it is stated what the container holds when it is full in litres or gallons. This refers to the volume of the interior space contained by the container, not the volume of space the container were to occupy if it was stored in my closet. (And we all know litres is just fancy talk for 1000 cubic centimetres or 0.001 cubic metres.)
I hope that helps clear up some of your queries.
- PeckyP -
