If the base radius of a cylinder is increased by 10% and the height remains unchanged, then find the percentage increase in the volume of the cylinder.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21%
The volume of a cylinder is \(\pi r^2h\); with \(h\) unchanged, the volume changes as the square of the radius.
New radius \(=1.1\times\) old radius
New volume \(=1.1^2=1.21\times\) old volume
Increase \(=1.21-1=0.21\), that is, 21%
Tip: A quantity that depends on the square of a length (area, or this volume) grows by \(\displaystyle 2x+\frac{x^2}{100}\) per cent when the length grows by \(x\%\): here \(20+1=21\%\), not 20%.