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: 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 1,000 and at the same time n is a perfect square and a perfect cube ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6

Answer: b


Question: Problem: in the coordinate plane , a circle centered on point ( 3 , - 4 ) passes through point ( 1 , 1 ) . what is the area of the circle ? 
Options: a ) 29 π , b ) 18 π , c ) 25 π , d ) 37 π , e ) 41 π

Answer: a


Question: Problem: a man walking at the rate of 6 km per hour crosses a square field diagonally in 9 seconds the area of the field is 
Options: ['a ) 110 sq . m', 'b ) 111.5 aq . m', 'c ) 112.5 sq . m', 'd ) 114 sq . m', 'e ) none of these']

Answer:
c