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

Example Input: Problem: a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 223 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ? 
Options: ['a ) 12541', 'b ) 12542', 'c ) 12544', 'd ) 12545', 'e ) can not be determined']
Example Output: c

Example Input: Problem: a wooden cube whose edge length is 8 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 ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %
Example Output: d

Example Input: Problem: consider a quarter of a circle of radius 20 . let r be the radius of the circle inscribed in this quarter of a circle . find r . 
Options: ['a ) 20 * ( sqr 2 - 1 )', 'b ) 8 * ( sqr 3 - 1 )', 'c ) 4 * ( sqr 7 - 1 )', 'd ) 12 * ( sqr 7 - 1 )', 'e ) none of these']
Example Output:
a