What is the perimeter of a quadrant of a circle of radius r?

It is given a quadrant of a circle of radius

r

.
The following figure depicts the given situation.

The radius of the circle is r.
The total circumference of the circle is

2 πr

.
So, we get,
Perimeter of a quadrant of a circle

= \frac{1}{4} \times 2 π \times r + 2 r

= \frac{πr}{2} + 2 r

= \frac{r}{2} [π + 4]

Thus, the perimeter of the quadrant of the circle is

\frac{r}{2} [π + 4]

.
Hence, the correct option is 3.

What is the perimeter of a quadrant of a circle of radius $r$ ?