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 :
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Step-by-Step Solution
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 2πr, where r is the radius.
Step 3: Substitute values and calculate arc length
Substitute the given radius r=7 cm and the value of π=722 into the arc length formula. This simplifies to 11 cm.
Step 4: Calculate the total perimeter
Add the calculated arc length to the lengths of the two radii (OA and OB), each 7 cm, to find the total perimeter of the quadrant.