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 ?

Solution (By Examveda Team)

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 :
$$\eqalign{ & = \left( {2\pi \times \frac{{9r}}{{10}} \times \frac{{23h}}{{20}}} \right) \cr & = \frac{{207}}{{200}} \times 2\pi rh \cr} $$
Increase in curved surface area :
$$\eqalign{ & = \left( {\frac{{207}}{{200}} \times 2\pi rh - 2\pi rh} \right) \cr & = \frac{7}{{200}} \times 2\pi rh \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{7}{{200}} \times 2\pi rh \times \frac{1}{{2\pi rh}} \times 100} \right)\% \cr & = 3.5\% \cr} $$