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

Correct option(D) 28 and 35

Explanation:

2(a + b) + ab = 16 ... (1)

2(b + c) + bc = 24 ... (2)

2(c + a) + ca = 31 ... (3)

From equation (2), equation (3) =>(a - b) (2 + c) = 7 ... (4)

From equation (2) and equation (4)  =>4a = 2 + 5b ... (5)

Solve equation (1) and (5)

b = 2 a = 3, c = 5

Volume = 30