SOLUTION: Fig. 4 shows a cone. The angle between the axis and the slant edge is 30�. Water is poured into the cone at a constant rate of 2 cm3 per second. At time t seconds, the radius of t

Question 1090347: Fig. 4 shows a cone. The angle between the axis and the slant edge is 30�. Water is poured into the
cone at a constant rate of 2 cm3 per second. At time t seconds, the radius of the water surface is r cm and the volume of water in the cone is V cm3.
Show that V= (sqrt3/3*pi*r^3) and find dv/dr
[You may assume that the volume of a cone of height h and radius r is (1/3*pi*r^2*h)]
I worked it out but could only prove that V= sqrt3/3*pi*r^2... why would h equal (sqrt 3 r) and not just sqrt 3?
Thank you ever so much!!!

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

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So then,

So then differentiating,

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