Question

The radius of a solid right circular cylinder decreases by $20\%$ and its height increases by $10\%$. Find the percentage change in its curved surface area

• A. Decrease $=$ $19\%$
• B. Decrease $=$ $12\%$
• C. Decrease $=$ $15\%$
• D. Decrease $=$ $13\%$

Answer 1

The correct option is B Decrease $=$ $12\%$

Given, a solid right circular cylinder whose radius is decreased by $20\%$ and height increased by $10\%$
Let radius of solid right circular cylinder be $r$ and height be $h$.
Then, curved surface area$=2\pi rh$
Decreased radius $=$ $r-$ $20\%$ $r=$ $0.8$ $r$
Increased height $=$ $h+$ $10\%$ $h=$ $1.1$ $h$
New Curved surface area $=2\pi rh$
$=2\times \pi \times 0.8r\times 1.1h$
$=1.76\pi rh$
New curved surface area is less than curved surface area. So, curved surface area is decreased.
$\%$ decreased $=\frac{C.S.A-NewC.S.A}{C.S.A}\times 100$ $\%$
$=\frac{2\pi rh-1.76\pi rh}{2\pi rh}\times 100$ $\%$
$=\frac{0.24\pi rh}{2\pi rh}\times 100$ $\%$
$=12$ $\%$