In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: what is the smallest positive integer nn such that √ 6,480 ∗ n is a perfect cube ? 
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
e

Problem: the ratio of the volumes of two cubes is 8 : 27 what is the ratio of their total surface areas ? 
Options: a ) 2 : 4 , b ) 3 : 6 , c ) 4 : 12 , d ) 4 : 9 , e ) 1 : 3
d

Problem: if y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer , then y must be 
Options: a ) 21 , b ) 10 , c ) 61 , d ) 72 , e ) 14

b