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 $261.5 \mathrm{~m}^{2}$.

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Updated on: 10-Oct-2022

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