Question

The arc length of a quarter circle with radius $r$ and diameter $d$ can be written as

• A. $2\mathrm{\pi r}$
• B. $\mathrm{\pi r}$
• C. $\frac{\mathrm{\pi d}}{2}$
• D. $\frac{\mathrm{\pi r}}{2}$

Answer 1

The correct option is D $\frac{\mathrm{\pi r}}{2}$

The arc length of a quarter circle with radius $r$ and diameter $d$ is nothing but ${\frac{1}{4}}^{th}$ the circumference of the circle. Hence, its length is given by:
$\frac{2\mathrm{\pi r}}{4}=\frac{\mathrm{\pi r}}{2}$