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 x , such that 7000 x is a perfect cube ? 
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
d

Problem: a rectangular block has the dimensions 5 x 6 x 7 cm it is dropped into a cylindrical vessel of radius 6 cm and height 10 cm . if the level of the fluid in the cylinder rises by 4 cm , what portion of the block is immersed in the fluid ? 
Options: ['a ) 22 / 7 x 24 / 35', 'b ) 22 / 7 x 36 x 4', 'c ) 22 / 7 x 36 / 5', 'd ) 22 / 7 x 37 / 21', 'e ) 22 / 7 x 32 / 21']
a

Problem: the length of a rectangle is reduced by 25 % . by what % would the width have to be increased to maintainthe original area ? 
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 33 % , e ) 40 %

d