Volume of Cone proof of formula

[heavenlyc1029]

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[neontiger63]

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[dobermans4lifexX]

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[zipperagogo2]

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[mediteight]

Place the top of the cone at the origin and the middle of the base at (h,0,0). Consider an infinitesimal disc perpendicular to the x axis between x and x+dx, with radius ax/h. Summing over all these discs from x=0 to x=h, gives the volume of the cone.

V=int[0->h](pi (ax/h)^2)dx =pi(a/h)^2 [(1/3) x^3][0->h] =pi a^2 h/3

[mathproblems]

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