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A rectangular piece is $ 20 \mathrm{~m} $ long and $ 15 \mathrm{~m} $ wide. From its four corners, quadrants of radii 3.5 $ \mathrm{m} $ have been cut. Find the area of the remaining part.
Given:
A rectangular piece is \( 20 \mathrm{~m} \) long and \( 15 \mathrm{~m} \) wide. From its four corners, quadrants of radii 3.5 \( \mathrm{m} \) have been cut.
To do:
We have to find the area of the remaining part.
Solution:
Length of the rectangular piece $(l) = 20\ m$
Length of the rectangular piece $(b) = 15\ m$
Radius of each quadrant $(r) = 3.5\ m$
$=\frac{7}{2}\ m$
Therefore,
Area of the rectangle $= l \times b$
$= 20 \times 15\ m^2$
$= 300\ m^2$
Area of 4 quadrants $= 4 \times \frac{1}{4} \pi r^2$
$=\frac{22}{7} \times(\frac{7}{2})^{2}$
$=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \mathrm{~m}^{2}$
$=\frac{77}{2} \mathrm{~m}^{2}$
$=38.5 \mathrm{~m}^{2}$
This implies,
Area of the remaining part $=300-38.5 \mathrm{~m}^{2}$
$=261.5 \mathrm{~m}^{2}$
The area of the remaining part is $261.5 \mathrm{~m}^{2}$.