In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
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Question: Problem: the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ? 
Options: a ) 43.0 , b ) 44.0 , c ) 43.5 , d ) 45.0 , e ) 42.0

Answer: a


Question: Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube ? 
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7

Answer: d


Question: Problem: the ratio of the volumes of two cubes is 729 : 343 . what is the ratio of their total surface areas ? 
Options: a ) 81 : 49 , b ) 81 : 122 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129

Answer:
a