Question

The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is __________.

Answer 1

The largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) will have its diameter equal to the breadth of the rectangle.



Let the radius of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) be r cm.

∴ Diameter of the circle = b

$$\begin{gathered} \Rightarrow 2r=b \\ \Rightarrow r=\frac{b}{2} \end{gathered}$$

∴ Area of the required circle $=\mathrm{\pi }{r}^2=\mathrm{\pi }{\left(\frac{b}{2}\right)}^2=\frac{\mathrm{\pi }{b}^2}{4}{\mathrm{cm}}^2$

The area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm (a > b) is $\underline{\frac{\mathrm{\pi }{b}^2}{4}{\mathrm{cm}}^2}$.