Question

A tank in the shape of an inverted right circular cone has height 8 meters and radius 12 meters. It is filled with 7 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is Δ = 1520 kg/m³

Answer 1

The work required to empty the tank is approximately 142,261,081.6π J.

Step-by-step explanation:

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

1. First, let's find the volume of the hot chocolate in the tank. The volume of a cone is given by V = πr²h/3, where r is the radius and h is the height. Substituting the values, we get V = π(12²)(7)/3 = 3768π m³.
2. Next, let's find the weight of the hot chocolate. The weight is given by W = density × volume × g, where density (Δ) is 1520 kg/m³ and g is the acceleration due to gravity (approximately 9.8 m/s²). Substituting the values, we get W = 1520 × 3768π × 9.8 = 17782635.2π N.
3. Finally, let's find the work required. Work is given by W = force × distance, where force is weight and distance is the height the hot chocolate needs to be lifted. Substituting the values, we get W = 17782635.2π × 8 = 142261081.6π J.

So, the work required to empty the tank is approximately 142,261,081.6π J.