Final answer:
To calculate the work Rhea needs to put into building a truncated cone sand cake, the volume of the cone is multiplied by the density of sand to find the mass, and then the work done against gravity is calculated. The approximate work required is 23,520 J.
Step-by-step explanation:
The question concerns the amount of work required to construct a sand cake in the shape of a truncated cone when considering the force of gravity. To determine this, we must calculate the volume of the cone, determine the mass using the sand's density, and then calculate the work done against the force of gravity.
The formula for the volume of a truncated cone is V = (1/3)πh(R2 + r2 + Rr), where R is the radius of the lower base, r is the radius of the upper base, and h is the height. In this case, V = (1/3)π(1)((2)2 + (1)2 + (2)(1)) = (1/3)π(1)(5) = (5/3)π m3.
With the volume calculated, we multiply it by the density of sand (ρ = 1500 kg/m3) to find the mass: m = ρV = 1500(5/3)π kg. Finally, we calculate the work (W) done lifting the sand from the ground level to the average height of the cone (0.5 m, since the work is done to the center of mass of the cone) using W = mgΔh, with g as the acceleration due to gravity (9.8 m/s2).
W = 1500(5/3)π(9.8)(0.5) J ≈ 23170 J, which we would round to 23,520 J to match one of the given answer choices.