If the height of a cylinder is increased by 15 percent and the radius of its base is decreased by 10 percent… · ABC26GN4907

Let original height $=h$ and original radius $=r$. $$\text { New height }=115 \% \text { of } h=\frac{23 h}{20} \text {. }$$ New radius $=90 \%$ of $r=\frac{9 r}{10}$. Original curved surface area $=2 \pi r h$. New curved surface area $=\left(2 \pi \times \frac{9 r}{10} \times \frac{23 h}{20}\right)=\frac{207}{200} \times 2 \pi r h$. Increase in curved surface area = $$\left(\frac{207}{200} \times 2 \pi r h-2 \pi r h\right)=\frac{7}{200} \times 2 \pi r h . \text { ∴ } \text { Increase } \%=\left(\frac{7}{200} \times 2 \pi r h \times \frac{1}{2 \pi r h} \times 100\right) \%=3.5 \% .$$