Question

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $14cm\times 7cm$. Find the area of the remaining card board. $[\text{Use}\pi =\frac{22}{7}]$

Answer 1

From the figure, we can conclude that the circles will be of the maximum area if their diameter is equal to $7cm.$

We need to calculate the area of the shaded region let us say it is $A.$

Area shaded $=$ Area of cardboard $-$ Area of circles

$\Rightarrow A=14\times 7-2\times \pi {\left(\frac{7}{2}\right)}^2$

$\Rightarrow A=98-2\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$

$\Rightarrow A=98-77$

$\Rightarrow A=21{cm}^2$

Hence, the remaining area of the cardboard is equal to $21{cm}^2.$