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: the largest four - digit number which is a perfect cube , is 
Options: ['a ) 8000', 'b ) 9261', 'c ) 9999', 'd ) none of these', 'e ) can not be determined']
b

Problem: a hall is 24 meters long and 12 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ? 
Options: ['a ) 1896', 'b ) 1912', 'c ) 2108', 'd ) 2304', 'e ) 2524']
d

Problem: a wooden cube whose edge length is 5 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ? 
Options: a ) 70.6 % , b ) 74.5 % , c ) 78.4 % , d ) 82.1 % , e ) 86.9 %

c