Question

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

Answer 1

The circles with maximum area and given condition will have diameter= 7cm

Area of circles=$\pi r^2+\pi r^2=\frac{22}{7}\times (\frac{7}{2}{)}^2+\frac{22}{7}\times (\frac{7}{2}{)}^2=\frac{77}{2}+\frac{77}{2}=77$

Area of cardboard $=14\times 7=98$ (Since it is a rectangle)

Remaining area $=98-77=21$ sq. units