Question

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

• A. $77\%$
• B. $87\%$
• C. $98\%$
• D. $55\%$
• E. $75\%$

Answer 1

The correct option is C $98\%$

Let each side of cuboid is $10$ unit.

Then initial volume of the cuboid $=$ length $\times$ breath $\times$ height

$=10\times 10\times 10=1000$ cubic unit

After increment dimension is

Length $=(10+10\%$ of $10)=11$

Breadth $=(10+20\%$ of $10)=12$

Height $=(10+50\%$ of $10)=15$

Now present volume $=11\times 12\times 15=1980$ cubic unit

Increase in volume $=1980-1000=980$ cubic unit

Percentage increase in volume $=\frac{980}{1000}\times 100=98\%$