The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

Question: The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

Solution:
Let each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= Length × Breadth × Height
= (10 × 10 × 10)
= 1000 cubic unit.

After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.

Now, New volume = (11 × 12 × 15) = 1980 cubic unit.

∴ Increase in volume = 1980 - 1000 = 980 cubic unit.
Increase in volume percent = (980/1000) × 100
= 98%