If the height of a cylinder is increased by 15 percent and the radius of its base is decreased by 10 percent then by what percent will its curved surface area change ?

Answer: Option B

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