instruction:
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
question:
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 4 m , the volume of the box ( in m 3 ) is : 
Options: a ) 4480 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960
answer:
a


question:
Problem: the product of the squares of two positive integers is 9 . how many pairs of positive integers satisfy this condition ? 
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
answer:
b


question:
Problem: amit and ian paint a wall in alternating shifts . first amit paints alone , then ian paints alone , then amit paints alone , etc . during each of his shifts , amit paints 1 / 2 of the remaining unpainted area of the wall , while ian paints 1 / 3 of the remaining unpainted area of the wall during each of his shifts . if amit goes first , what fraction of the wall ' s area will remain unpainted after amit has completed his 6 th shift ? 
Options: ['a ) 1 / 27', 'b ) 1 / 54', 'c ) 1 / 81', 'd ) 1 / 162', 'e ) 1 / 486']
answer:

e