instruction:
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
question:
Problem: in triangle pqr , the angle q = 90 degree , pq = 3 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 3.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
answer:
b

question:
Problem: the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?
Options: ['a ) 50 %', 'b ) 60 %', 'c ) 75 %', 'd ) 80 %', 'e ) 89 %']
answer:
c

question:
Problem: find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 11 cm and 9 cm ?
Options: a ) 100 cm 2 , b ) 150 cm 2 , c ) 333 cm 2 , d ) 400 cm 2 , e ) 750 cm 2
answer:
d