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What values must the constants take? Can you identify each curve in the following accurately drawn chart?
These curves are now used to design some mathematical vessels of height 10 by rotating the curves about the y axis. Assuming that x and y are measured in centimetres, what are the volumes of the vessels?
Water is poured slowly at a rate of 1cm^3 per minute into these vessels. At what depth of water, to the nearest mm, will each of them be half full? Do your results make sense from the diagram?
Brimful
Age 16 to 18
Challenge Level 
Constants A, B, C, D are chosen so that the following 4 curves pass through the point (2.5, 10) y = Ax\quad y = Bx^2 \quad y = Cx^3\quad y = Dx^4+x
What values must the constants take? Can you identify each curve in the following accurately drawn chart?
These curves are now used to design some mathematical vessels of height 10 by rotating the curves about the y axis. Assuming that x and y are measured in centimetres, what are the volumes of the vessels?
Water is poured slowly at a rate of 1cm^3 per minute into these vessels. At what depth of water, to the nearest mm, will each of them be half full? Do your results make sense from the diagram?
