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Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $14\ cm\times 7\ cm$. Find the area of the remaining card board.
Given: Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $14\ cm\times 7\ cm$
To do: To find the area of the remaining card board.
Solution:
Here given dimension of the card board $=14cm\times 7\ cm$
$\because$ Maximum area of circles, touching each other from the rectangular card board is cut out,
Diameter of each piece $=\frac{length\ of\ the\ card\ board}{2}$
$\therefore$ Radius of each piece $=\frac{diameter}{2}$
$=\frac{7}{2}\ cm$
$\Rightarrow$ Area of each piece $=\pi r^{2} =\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}$
$=\frac{77}{2}\ cm^{2}$
$\therefore$ Total area cut out from the card boad $=$sum of the areas of both pieces
$=\frac{77}{2} +\frac{77}{2}$
$=74\ cm^{2}$
$\Rightarrow$ Area of the remaining card board$=$Area of the card board$-$Area cut out from card board
$=98\ cm^{2} -74\ cm^{2}$
$=24\ cm^{2}$
Therefore, Area of the remaining card board $=24\ cm^{2}$.
Updated on: 10-Oct-2022
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