Question

The diameter of a cylinder jar is increased by 25%. By what percent must the height of the jar be decreased so that there is no change in its volume?

• A. 56.25 %
• B. 54%
• C. 36 %
• D. 64%

Answer 1

The correct option is C

36 %

Volume of a cylinder = $(\pi \times r^2\times h)$

Diameter is increased by 25 % hence radius of the cylinder is also increased by 25 %.

As per the question, volume remains the same that means height should be decreased.

Let the new height be h’.

After the increment of radius of cylinder volume = $(\pi \times (1.25r{)}^2\times h^{\prime })$.

Equating both the equation, we have,

$(\pi \times r^2\times h)$ = $(\pi \times (1.25r{)}^2\times h^{\prime })$

$\Rightarrow h=\frac{25}{16}{h}^{\prime }$

$\Rightarrow \frac{h^{\prime }}{h}=\frac{16}{25}$

$\Rightarrow \left[\frac{h–h^{\prime }}{h}\right]$ $\times 100\%$ = $(25-\frac{16}{25})$ $\times 100\%$ $=36\%$

$\Rightarrow Heightdecrement=36\%$