Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2006 · Marks: · Difficulty:
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 percent decrease
(b)3.5 percent increase
(c)5 percent decrease
(d)5 percent increase
Answer
Answer (as printed): B
Explanation
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 = $$\left(\frac{207}{200} \times 2 \pi r h-2 \pi r h\right)=\frac{7}{200} \times 2 \pi r h . \text { ∴ } \text { Increase } \%=\left(\frac{7}{200} \times 2 \pi r h \times \frac{1}{2 \pi r h} \times 100\right) \%=3.5 \% .$$
Explanation as extracted from the printed page; notation may be imperfect.