A tank in the shape of an inverted right circular cone has height 7 meters and r

Question

A tank in the shape of an inverted right circular cone has height 7 meters and radius 13 meters. It is filled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is ?=1450kg/m3 and we are using weight-density.

Explanation / Answer

Note that, by similar triangles, the equation that relates the radius, r, to the height, h, is: r/h = 13/7 ==> h = 7/13 * r The volume of a slab of chocolate at a distance of x from the bottom of the tank is then: dV = 1/3 pi r^2 (h_i - h_f) = 1/3 * 22/7 * (5-7)/13 * r^3 = 2478.66 W = p*dV = 1450 *2478.66 =3594057 Kg

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