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 ?
A. 3.5% decrease
B. 3.5% increase
C. 5% decrease
D. 5% increase
Answer: Option B
Solution(By Examveda Team)
Let original height = h and original radius = rNew 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 % :
$$\eqalign{ & = \left( {\frac{7}{{200}} \times 2\pi rh \times \frac{1}{{2\pi rh}} \times 100} \right)\% \cr & = 3.5\% \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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