UPSC CAPF Assistant Commandant Model Paper 6

GIVEN:
Surface area of a cuboid = 376 cm2
Ratio of length, breadth, and height of the cuboid = 5 : 4 : 3
CONCEPT:
Area and volume of 2-D and 3-D shapes.
FORMULA USED:
Surface area of cuboid = 2(lb + bh + lh)
Diagonal of cuboid = √ (l2+b2+h2)
Diagonal of cube = a√3
CALCULATION:
Let the length, breadth, and height of the cuboid are ‘5x’, ‘4x’, and ‘3x’ respectively.
According to the question,
2[(5x × 4x) + (4x × 3x) + (5x × 3x)] = 376
⇒2[20x2+12x2+15x2]=376
⇒ x = 2
So, the length, breadth and height of the cuboid are 10 cm, 8 cm, and 6 cm respectively.
Now,
The main diagonal of the cuboid = √ (102+82+62) = 10√2 cm
⇒ The side of the cube = 10√2 cm
∴ Main diagonal of the cube = 10√2 × √3 = 10√6 cm