The shortest distances between an interior diagonal of a rectangular parallelepiped P, and the edges it does not meet are 25 ,  3013 and 1510 . Then the volume of the parallelepiped is

aba2+b2=25⇒1a2+1b2=120→(i) bcb2+c2=3013⇒1b2+1c2=13900→(ii) cac2+a2=1510⇒1c2+1a2=10225→(iii) (i)+(ii)-(iii)⇒2b2=18900⇒b2=100⇒b=10 from  (i)⇒1a2=4100⇒a2=25⇒a=5 from  (iii)⇒1c2=4900⇒c2=225⇒c=15 volume=abc=5(10)15=750