On each face of a cuboid, the sum of its perimeter and its area is written. Among the six numbers so written, there are three distinct numbers and they are 16,24 and 31 . The volume of the cuboid lies between

Step-by-step solution

2(a+b)+a b=16 (1)2(b+c)+b c=24 (2)2(c+a)+c a=31 (3) From equation (2) , equation (3) (a-b)(2+c)=7 (4) From equation (2) and equation (4) 4 a=2+5 b (5) Solve equation (1) and (5)b=2 a=3, c=5 Volume =30