Question

What is the perimeter of a quadrant of a circle with radius r=3cm?

Answer 1

Hint: We are given with data that involves the radius of a circle. We are asked to find the perimeter of the quadrant that is $${\displaystyle \frac{1}{4}}$$ part of a circle. So for that we can divide the perimeter of the full circle by 4. So for the perimeter of a quadrant the formula is $${\displaystyle \frac{2\pi r}{4}}+2r$$. We will just place the value of radius so given and find the perimeter of the quadrant.

Complete step by step answer:
Let us first draw the diagram of the given situation.

Thus the coloured portion is called the quadrant of the circle.
Now let's find the perimeter.
$$={\displaystyle \frac{2\pi r}{4}}$$+$$2r$$
Putting the value of the radius we can find the perimeter.
$$={\displaystyle \frac{2\times 3.14\times 3}{4}}+2\times 3={\displaystyle \frac{18.84}{4}}+6=10.71cm$$
Thus the perimeter of the quadrant is 10.71cm

Note:
Note that perimeter is the addition of the lengths of the edges or sides of the diagram. Since a circle has no edge its circumference is the only perimeter. Also note that perimeter is always measured in a single unit that is cm or m and not square quantity since it is a type of length.