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

Given:

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions \( 14 \mathrm{~cm} \times 7 \mathrm{~cm} \). 

To do: 

We have to find the area of the remaining card board.

Solution:

Length of the rectangle $= 14\ cm$

Breadth of the rectangle $= 7\ cm$

Area of the rectangle $=14 \times 7$

$=98 \mathrm{~cm}^{2}$

Radius of each circle $=\frac{7}{2} \mathrm{~cm}$

Area of two circles $=2 \pi r^{2}$

$=2 \times \frac{22}{7} \times (\frac{7}{2})^2$

$=77 \mathrm{~cm}^{2}$

Area of the remaining portion $=$ Area of the rectangle $-$ Area of two circles

$=98-77$

$=21 \mathrm{~cm}^{2}$

The area of the remaining card board is $21\ cm^2$.

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Updated on: 10-Oct-2022

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