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Hint: - Here we go through by the formula of circumference of a circle to find out the radius of the circle then by the help of the radius we easily find out the area of a quadrant of a circle.

Complete step-by-step answer:

Here in the question the circumference of the circle is given as 22cm.

As we know that the circumference of circle$ = 2\pi r$. By equating this formula with the data given in the question we will find out the value of radius(r).

I.e. $2\pi r = 22cm$ and we know that value of $\pi = \dfrac{{22}}{7}$

$

\Rightarrow 2 \times \dfrac{{22}}{7} \times r = 22 \\

\Rightarrow r = \dfrac{{22 \times 7}}{{2 \times 22}} \\

\therefore r = 3.5 \\

$

And now we have to find the area of a quadrant of a circle.

As we know that area of a quadrant circle$ = \dfrac{{\pi {r^2}}}{4}$

Now put the value of radius in the formula to find out the area. i.e.

$

= \dfrac{{\pi {{\left( {3.5} \right)}^2}}}{4} \\

= \dfrac{{22}}{7} \times \dfrac{{{{\left( {3.5} \right)}^2}}}{4} \\

= \dfrac{{22 \times 12.25}}{{28}} \\

= 9.625c{m^2} \\

$

Hence the area of a quadrant of a circle is $9.625c{m^2}$.

Note:-Whenever we face such a type of question the key concept for solving the question is to first find out the terms which we need that are helpful for finding the answer. Here we have to first find out the value of radius for calculating the area of the quadrant of the circle. And we also know that quadrant of a circle means one fourth of a circle.

Complete step-by-step answer:

Here in the question the circumference of the circle is given as 22cm.

As we know that the circumference of circle$ = 2\pi r$. By equating this formula with the data given in the question we will find out the value of radius(r).

I.e. $2\pi r = 22cm$ and we know that value of $\pi = \dfrac{{22}}{7}$

$

\Rightarrow 2 \times \dfrac{{22}}{7} \times r = 22 \\

\Rightarrow r = \dfrac{{22 \times 7}}{{2 \times 22}} \\

\therefore r = 3.5 \\

$

And now we have to find the area of a quadrant of a circle.

As we know that area of a quadrant circle$ = \dfrac{{\pi {r^2}}}{4}$

Now put the value of radius in the formula to find out the area. i.e.

$

= \dfrac{{\pi {{\left( {3.5} \right)}^2}}}{4} \\

= \dfrac{{22}}{7} \times \dfrac{{{{\left( {3.5} \right)}^2}}}{4} \\

= \dfrac{{22 \times 12.25}}{{28}} \\

= 9.625c{m^2} \\

$

Hence the area of a quadrant of a circle is $9.625c{m^2}$.

Note:-Whenever we face such a type of question the key concept for solving the question is to first find out the terms which we need that are helpful for finding the answer. Here we have to first find out the value of radius for calculating the area of the quadrant of the circle. And we also know that quadrant of a circle means one fourth of a circle.