Three college students are trapped in deep snow in northern Canada. To survive they must build an igloo using snow large enough for all of them to fit and small enough to not exceed their strength and stamina. Luckily one of them is a math major and quickly formulates the dimensions of the blocks they need to cut out from the hard packed snow. Because he doesn't know what each block will weigh until they cut it, he quickly calculates an igloo built with 200 blocks, and then again with 300 blocks, and 500 blocks to have the dimensions ready to begin construction immediately. He decides that to house all of them quickly the igloo should be 10 meters in diameter and 5 meters tall at its tallest point. Give the dimensions of the blocks and the formula for construction with 200 blocks, with 300 blocks, and with 500 blocks.
The dimensions of cubes needed to form an igloo are calculated. A diagram is provided.