Question

The diameter of a right circular cylinder is decreased by $10\%$ The volume of the cylinder remains the same then the percentage increase in height is:

• A. $20\%$
• B. $23.45\%$
• C. $5\%$
• D. $20.5\%$

Answer 1

The correct option is B

$23.45\%$

Step 1:- Find the volume of the cylinder initially.

Let initially the base radius of the cylinder$=100\mathrm{unit}$

The height of the cylinder $=100\mathrm{unit}$

Initial Volume $={\mathrm{\pi r}}^2\mathrm{h}$$=\mathrm{\pi }\times {100}^2\times 100$

Step 2:- Find the volume of the cylinder diameter decreased

Let later the base radius of the cylinder$=90\mathrm{unit}$

The height of the cylinder $=\mathrm{h}\mathrm{unit}$

later Volume $={\mathrm{\pi r}}^2\mathrm{h}$ $=\mathrm{\pi }\times {90}^2\times \mathrm{h}$

According to the condition we can say that

$\mathrm{\pi }\times {90}^2\times \mathrm{h}$$=\mathrm{\pi }\times {100}^2\times 100$

$\mathrm{h}=\frac{100\times 100\times 100}{90\times 90}=\frac{10000}{81}$

$\mathrm{h}=123.45$

Step 3:- Find the percentage increase

$\mathrm{percentage}\mathrm{increase}=\frac{\mathrm{Change}\mathrm{in}\mathrm{value}}{\mathrm{inital}\mathrm{value}}\times 100$

$\mathrm{percentage}\mathrm{increase}=\frac{(123.45-100)}{100}\times 100$

$\mathrm{percentage}\mathrm{increase}=23.45\%$

Hence, he percentage increase in height is $23.45\%$