A circular arc whose radius is 4 cm makes an angle 45° at the centre. Find the perimeter of the sector formed.

(Take p = $\frac{22}{7}$)

To find the perimeter of the sector formed by the circular arc, we need to calculate the sum of the length of the arc and the two radii that bound the sector.

First, let's identify the given values:
Radius of the circular arc, r = 4 cm
Angle subtended at the centre, $\theta$ = 45°
We are given $\pi =\frac{22}{7}$

The formula for the length of an arc (l) of a sector is:
$l=\frac{\theta }{360}\times 2\pi r$

Substituting the given values into the formula:
$l=\frac{45}{360}\times 2\times \frac{22}{7}\times 4$
Simplifying the fraction $\frac{45}{360}$:
$\frac{45}{360}=\frac{1}{8}$
Now, substitute this back:
$l=\frac{1}{8}\times 2\times \frac{22}{7}\times 4$
$l=\frac{1\times 2\times 22\times 4}{8\times 7}$
Since $2\times 4=8$, these terms cancel out with the 8 in the denominator:
$l=\frac{22}{7}$ cm

The perimeter of the sector is the sum of the arc length and the two radii:
Perimeter = Arc length + 2 $\times$ Radius
Perimeter = $l+2r$
Perimeter = $\frac{22}{7}+2\left(4\right)$
Perimeter = $\frac{22}{7}+8$

To add these terms, find a common denominator:
Perimeter = $\frac{22}{7}+\frac{8\times 7}{7}$
Perimeter = $\frac{22}{7}+\frac{56}{7}$
Perimeter = $\frac{22+56}{7}$
Perimeter = $\frac{78}{7}$ cm

Therefore, the correct option is $\frac{78}{7}$ cm.