Question

The areas of three adjacent faces of a cuboid are in the ratio 7 ∶ 10 ∶ 14. If the volume of cuboid is 350 cm³, then the longest side has a length of
1. 7 cm
2. 14 cm
3. 10 cm
4. 20 cm

Answer 1

Correct Answer - Option 3 : 10 cm

Concept:

Volume of cuboid = length × breadth × height

Calculation:

Let the edges of the cuboid be a, b, and c.

Since the areas of three adjacent faces are in the ratio 7 : 10 : 14,

⇒ ab : bc : ca = 7 : 10 : 14

∴ ab : bc = 7 : 10

⇒ a : c = 7 : 10      

Also, bc : ca = 10 : 14

⇒ b : a = 10 : 14 = 5 : 7   

⇒ a : b = 7 : 5      

∴ a : b : c = 7 : 5 : 10

Let the ratios be 7x, 5x and 10x.

⇒ Volume of cuboid = 350 cm³ 

⇒ abc = 350

⇒ (7x) × (5x) × (10x) = 350

⇒ x³ = 1

⇒ x = 1

So, the edges are 7 cm, 5 cm and 10 cm.

Hence, the longest side has the length 10 cm.