### The length, breadth and height of a room in the shape of a cuboid are increased by 20%, 25% and 30% respectively. Find the percentage change in the volume of the cuboid.

**घनाभ के आकार के एक कमरे की लंबाई, चौड़ाई और ऊंचाई में क्रमशः 20%, 25% और 30% की वृद्धि की जाती है। घनाभ के आयतन में प्रतिशत परिवर्तन ज्ञात कीजिए।**

a) 105% Decrease

b) 95% Increase

c) 90% Decrease

d) 85% Increase

**Ans : b) 95% Increase**

UP Police SI Exam : Mathematics

### Solution

To find the percentage change in the volume of the cuboid when its dimensions are increased, we can use the formula for the volume of a cuboid and apply the percentage increases.

Let’s denote the original length, breadth, and height of the cuboid as ( l ), ( b ), and ( h ) respectively. The original volume ( V ) is given by:

After increasing the dimensions:

- New length =
- New breadth =
- New height =

The new volume ( V’ ) is:

Simplifying this:

So, the new volume ( V’ ) is:

The percentage change in volume is:

Percentage change = (1.95 – 1) x100%

Percentage change = 0.95 x 100%

Percentage change = 95%