Question

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

(a) 7 and 14

(b) 14 and 21

(c) 21 and 28

(d) 28 and 35

Answer 1

Answer is : (d) 28 and 35

Let the length, breadth and height of cuboid be x, y and z respectively.

∴ Perimeter of face PQRS = 2(x+y)

Area of PQRS = xy

∴ 2(x+y) + xy = 16 …(i)

Similarly, for face APSD,

2(y+z) + yz = 24 …(ii)

and for face APQB,

2(x+z) + xz = 31 …(iii)

From Eqs. (ii) and (iii), we get

(x - y)(2+z) = 7 …(iv)

From Eqs. (ii) and (iv), we get

4x = 2+5y …(v)

On solving Eqs. (i) and (v), we get

x = 3, y = 2, z = 5

∴ Volume of cuboid = xyz = 3 x 2 x 5 = 30

Hence, option (d) is correct.