Question

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

Answer 1

Dimension of the rectangular card board = $14cm\times 7cm$

Since, two circular pieces of equal radii and maximum area touching each other are cut from the rectangular card board, therefore, the diameter of each of each circular piece is $\frac{14}{2}=7cm$

Radius of ech circular piece = $\frac{7}{2}cm$
$\therefore$ Sum of area of two circular pieces $=2\times \pi (\frac{7}{2}{)}^2=2\times \frac{22}{7}\times \frac{49}{4}=77c{m}^2$
Area of the remaining card board = Area of the card board - Area of two circular pieces
$=14cm\times 7cm-77c{m}^2=98c{m}^2-77c{m}^2=21c{m}^2$
Thus, the area of the remaining card board is $21c{m}^2$