Question

If the perimeter of a quadrant of a circle is $25\text{cm}$, then the radius of the circle is

• A. $14\text{cm}$
• B. $7\text{cm}$
• C. $3.5\text{cm}$
• D. $28\text{cm}$

Answer 1

The correct option is B $7\text{cm}$

Let $r$ be the radius of the quadrant of a circle.

Given that the perimeter of quadrant of a circle is $25\text{cm}$.
$\therefore$ Perimeter of quadrant $=\frac{2\pi r}{4}+2r$
$\Rightarrow 25=\frac{\pi r}{2}+2r$
$\Rightarrow 25=(\frac{22}{7}\times \frac{1}{2}+2)r$
$\Rightarrow 25=\left(\frac{11+14}{7}\right)\times r$
$\Rightarrow r=7\text{cm}$
Therefore, the radius of the circle is $7\text{cm}$.

Hence, the correct answer is option b.