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:
$ V = l \times b \times h $

After increasing the dimensions:

• New length = $ l \times 1.20 $
• New breadth = $ b \times 1.25 $
• New height = $ h \times 1.30 $

The new volume ( V’ ) is:
$ V’ = (l \times 1.20) \times (b \times 1.25) \times (h \times 1.30) $

Simplifying this:

$ V’ = l \times b \times h \times 1.20 \times 1.25 \times 1.30 $
$ V’ = V \times 1.20 \times 1.25 \times 1.30 $

So, the new volume ( V’ ) is:
$ V’ = V \times 1.95 $

The percentage change in volume is:

Percentage change = (1.95 – 1) x100%
Percentage change = 0.95 x 100%
Percentage change = 95%