Question

You go to an ice cream shop and notice that you can get a cone or a banana split. The cone is filled with ice cream and then you get a half sphere on top, whose diameter is the same as the diameter of the cone. The banana split comes with 3 full spheres of ice cream. If the spheres all come from the same ice cream scoop and the height of the cone is 3 times its diameter, what is the ratio of ice cream you get in the banana split compared to the cone? a) 3:2 b) 4:3 d) e) 5:3 Answer is not there

Answer 1

1)

ice cream in Banana split =3*volume of one sphere =3*(4/3)*$\pi$r³ =4$\pi$r³

ice cream in cone =(1/3)*$\pi$r²h+(2/3)*$\pi$r³ =(1/3)*$\pi$r²*6r+(2/3)*$\pi$r³ =(8/3)$\pi$r³

hence ratio of ice cream in banana split to cone =4$\pi$r³/((8/3)$\pi$r³)=3 :2

option A

2)

option D is correct