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September 3, 2014

September 3, 2014

Posted by **Abhi** on Sunday, July 1, 2012 at 2:17pm.

- Rate measure -
**Damon**, Sunday, July 1, 2012 at 3:18pmI assume that h is the height of the cone from the floor to the base of the hemisphere. Thus the diameter of the cone at the floor is 2 h and the height of the cone if it went to the tip would be 2 h

volume of cone of base diameter 2 h and height 2 h:

(1/3)(2h)(pi/4)(4 h^2)= (2/3)pi h^3

volume of cut off tip of cone:

(1/3)(h)(pi/4)h^2 = (1/12) pi h^3

so

volume of cone base = (7/12)pi h^3

now

volume of hemisphere = (1/2)(4/3)pi(h/2)^3 = pi h^3/12

so

total balloon volume = (2/3) pi h^3

dV/dh = 2 pi h^2

dV/dt = dV/dh * dh/dt

so

dV/dt = 2 pi h^2 dh/dt

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