If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → decreases by 4%
The volume of a cuboid is length × breadth × height. The height is not changed, so the volume changes in the same ratio as length × breadth.
New length \(=1.2\,l\) (20% more) and new breadth \(=0.8\,b\) (20% less)
New volume \(=1.2\,l\times0.8\,b\times h=0.96\,lbh\)
The volume is now 96% of what it was, so it decreases by 4%
Tip: A rise and a fall by the same percentage never cancel: the result is always a fall of \(\frac{x^2}{100}\%\), here \(\frac{20^2}{100}=4\%\). That is why “remains unchanged” (Option 1) is wrong.