OACB is a quadrant of a circle with centre O and radius 7 cm where ACB is the arc. Then the perimeter of the quadrant is :

Step 1: Identify components of the perimeter

A quadrant of a circle is one-fourth of a full circle. Its perimeter consists of the curved arc and two straight radii that form the right angle at the center.

Step 2: Calculate the length of the arc

The length of the arc of a quadrant is one-fourth of the circumference of the full circle. The formula for the circumference of a circle is $2\pi r$, where $r$ is the radius.

Step 3: Substitute values and calculate arc length

Substitute the given radius $r = 7\text{ cm}$ and the value of $\pi = \frac{22}{7}$ into the arc length formula. This simplifies to $11\text{ cm}$.

Step 4: Calculate the total perimeter

Add the calculated arc length to the lengths of the two radii (OA and OB), each $7\text{ cm}$, to find the total perimeter of the quadrant.

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