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. (Use $\pi =\frac{22}{7}$)

Answer 1

Since each circle has maximum area,
diameter of each circle = half of length = 7 cm
radius of each circle = 3.5 cm

Area of each circle = $\pi$ x $r^2$

= $\frac{22}{7}$ x r x r

= $\frac{22}{7}$ x 3.5 x 3.5

= 38.5 $c{m}^2$

Then area of both circles will be = (38.5) x 2

=77 cm²

Total area = (14). (7)

=98 $c{m}^2$

Hence remaining area =98-77

= 21$c{m}^2$