Answer:Part A) The volume of the ice cream scoop is [tex]36\pi\ in^{3}[/tex]Part B) The melted ice cream won't fill the cupPart C) The melted ice cream exceeds the volume of Anna's cupPart D) The height of the smallest cylindrical cup is [tex]h=8\ in[/tex]Step-by-step explanation:Part A) Find the volume of the ice cream scoopwe know thatThe volume of the sphere (ice cream scoop) is equal to[tex]V=\frac{4}{3}\pi r^{3}[/tex]we have[tex]r=3\ in[/tex]substitute[tex]V=\frac{4}{3}\pi (3)^{3}=36\pi\ in^{3}[/tex]Part B) Find the volume of Anna's cylindrical cupwe know thatThe volume of a cylinder is equal to[tex]V=\pi r^{2}h[/tex]we have[tex]r=3\ in[/tex][tex]h=6\ in[/tex]substitute[tex]V=\pi (3)^{2}(6)=54\pi\ in^{3}[/tex][tex]54\pi\ in^{3}> 36\pi\ in^{3}[/tex]The volume of Anna's cup (cylinder) is greater than the volume of melted ice cream scoopthereforeThe melted ice cream won't fill the cup.Part C) Will two scoop of melted ice cream fit in Anna's cup?Multiply the volume of ice cream scoop by 2 and compare with the volume of Anna's cupso[tex](2)36\pi\ in^{3}=72\pi\ in^{3}[/tex][tex]72\pi\ in^{3}> 54\pi\ in^{3}[/tex]The volume of Anna's cup (cylinder) is less than the volume of two melted ice cream scooptherefore The melted ice cream exceeds the volume of Anna's cupPart D) Find the smallest cylindrical cup that will hold two scoops of melted ice creamwe know thatThe volume of a cylinder is equal to[tex]V=\pi r^{2}h[/tex]we have[tex]V=72\pi\ in^{3}[/tex] ------> volume of two scoops of melted ice cream[tex]r=3\ in[/tex]substitute in the formula and solve for h[tex]72\pi=\pi (3)^{2}h[/tex]simplify[tex]72=(9)h[/tex][tex]h=8\ in[/tex]