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

[EX Q]: Problem: a crate measures 2 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ? 
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
[EX A]: a

[EX Q]: Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 sq . cm , what is the length of the rectangle ? 
Options: a ) 15 cm , b ) 18 cm , c ) 21 cm , d ) 24 cm , e ) 27 cm
[EX A]: c

[EX Q]: Problem: if y is the smallest positive integer such that 7,700 multiplied by y is the square of an integer , then y must be 
Options: a ) 29 , b ) 58 , c ) 63 , d ) 74 , e ) 77
[EX A]:
e