Examveda

# 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.

A. 77%

B. 75%

C. 88%

D. 98%

E. 99%

### Solution(By Examveda Team)

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, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
% increase in volume = $$\frac{{980}}{{1000}} \times 100 = 98\%$$

Mind Calculation Method:
100 == 50%↑(height effects) ==> 150 == 20%↑(breadth) ==> 180 == 10%↑(length effects) ==> 198
Change in volume = 98%
[We can take net percentage change in any order]