The approximated value of the area of the given quarter of the circle is [tex]7.7\rm \; cm^2[/tex].
Given:
A quarter-circle is given. The radius of the quarter-circle is [tex]r=3[/tex] cm.
The quarter-circle is one-fourth part of a circle. So, its area will be equal to one-fourth of the area of the circle.
So, the area of the given quarter can be calculated as,
[tex]A=\dfrac{1}{4}\pi r^2\\A=\dfrac{1}{4}\pi (3)^2\\A=\dfrac{1}{4}\pi 9\\A=7.068\\A\approx 7.7\rm \; cm^2[/tex]
Therefore, the approximated value of the area of the given quarter of the circle is [tex]7.7\rm \; cm^2[/tex].
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