| If the height of a cylinder is increased by 15% and the radius of its base is decrease by 10%, then by what per cent will its curved surface areas change? [SSC (CPO) 2006] |
A) 3.5% decrease
B) 3.5% increase
C) 5% increase
D) 5% decrease
Correct Answer: B
Solution :
| Let height of cylinder be h and radius be r. |
| Then, curved surface area \[=2\pi rh\] |
| Now, height \[(h')=h+\frac{15}{100}h=\frac{23\,\,h}{20}\] |
| and radius \[(r')=r-\frac{10}{100}r=\frac{9r}{10}\] |
| Now, curved surface area \[=2\pi r'h'\] |
| \[=2\pi \left( \frac{9r}{10} \right)\left( \frac{23h}{20} \right)=2\pi \frac{(207)\,rh}{200}\] |
| Change in curved surface area |
| \[=\left( \frac{2\pi \times \frac{207\,\,rh}{200}-2\pi rh}{2\pi rh} \right)\times 100\] |
| \[=\frac{7}{200}\,\times \]=3.5% increase |
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