Question

If the length, breadth and height of a cuboid are in the ratio 9:6:4. Its lateral surface area is
480 cm? Find its volume.

Answer 1

✫ The volume of cuboid is 1728 cm² ✫

Step-by-step explanation:

Where,

• Length of cuboid = l
• Breadth of cuboid = b
• Height of cuboid = h

➽ l:b:h = 9:6:4

• Lateral surface area(LSA) of cuboid = 480 cm
• l = 9x
• b = 6x
• h = 4x

➽ LSA of cuboid = 2h(l + w)

➽ LSA of cuboid = 2×4x(9x+6x)

➽ LSA of cuboid = 8x(15x)

➽ LSA of cuboid = 120x²

Now,

• 120x² = 480
• x² = 480/120
• x² = 4
• x = √4
• x = 2

Therefore,

• l = 9 × 2 = 18
• b = 6 × 2 = 12
• h = 4 × 2 = 8

Then,finding the volume of cuboid,

➽ Volume of cuboid = lbh

➽ Volume of cuboid = 18 × 12 × 8

➽ Volume of cuboid = 1728 cm²