question_answer

Is the area of the circle inscribed in a square of side a cm is ............ .

A) \[\pi {{a}^{2}}c{{m}^{2}}\]

B) \[\frac{\pi {{a}^{2}}}{2}c{{m}^{2}}\]

C) \[\frac{\pi {{a}^{2}}}{4}c{{m}^{2}}\]

D) \[2\pi {{a}^{2}}c{{m}^{2}}\]

Correct Answer: C

Solution :

Let ABCD be a square of side a. \[\therefore \] Diameter of circle = Side of square = a      \[\therefore \] Radius of circle \[=\frac{a}{2}\] \[\therefore \]Area of circle \[=\pi {{\left( Radius \right)}^{2}}\] \[=\pi {{\left( \frac{a}{2} \right)}^{2}}=\frac{\pi {{a}^{2}}}{4}\] Hence, area of the circle is \[\frac{\pi {{a}^{2}}}{4}c{{m}^{2}}\]