A tank in the shape of an inverted right circular cone has height 10 meters and radius 16 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 δ= 1450kg/m3

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To find the work required to empty the tank, we need to calculate the force required to lift the hot chocolate to the top of the tank and then multiply it by the distance it needs to be lifted.

1. Calculate the mass of the hot chocolate:
The volume of the inverted cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height of the cone.
The volume of the hot chocolate is 5 cubic meters.
So, 5 = (1/3) * π * 16^2 * h.
Solve this equation for h to find the height of the hot chocolate in the cone.

2. Calculate the mass of the hot chocolate using its density:
Mass = Density * Volume.
The density of hot chocolate is given as δ = 1450 kg/m^3.
Calculate the mass of the hot chocolate using the obtained volume and density.

3. Calculate the weight of the hot chocolate:
Weight = Mass * Gravitational force.
The gravitational force is approximately 9.8 m/s^2.

4. Calculate the work required:
Work = Weight * Distance.
The distance is equal to the height of the cone.

5. Substitute the known values and calculate the work required to empty the tank.

Please note that this calculation assumes there is no friction or other external forces acting on the hot chocolate as it is being pumped out of the tank.