Question

If the diameter of a circle decreases to its $\frac{1}{4}$th, then its radius decreases to:

• A. $\frac{1}{2}$
• B. $4$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$

Answer 1

The correct option is D $\frac{1}{8}$

Let diameter of circle be $x$.

Then, radius of a circle will be $\frac{x}{2}.$

$\Rightarrow$ The diameter of circle decreases to its $\frac{1}{4}$.

$\therefore$ Decreased diameter $=x-\frac{x}{4}=\frac{4x-x}{4}=\frac{3x}{4}$.

$\Rightarrow$ Decreased in radius $=\frac{x}{2}-\frac{3x}{8}$ $=\frac{4x-3x}{8}$ $=\frac{x}{8}$ .

$\therefore$ Required answer is $\frac{1}{8}$.

Hence, option $D$ is correct.