**Question:**

A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m have been cut. Find the area of the remaining part.

**Solution:**

It is given that the length of the rectangular piece is $20 \mathrm{~m}$ and its width is $15 \mathrm{~m}$.

And, from each corner a quadrant each of radius $3.5 \mathrm{~m}$ has been cut out.

A rough figure for this is given below :

$\therefore$ Area of the remaining part $=$ Area of the rectangular piece $-(4 \times$ Area of a quadrant of radius $3.5 \mathrm{~m})$Now, area of the rectangular piece $=20 \times 15=300 \mathrm{~m}^{2}$

And, area of a quadrant with radius $3.5 \mathrm{~m}=\frac{1}{4} \pi \mathrm{r}^{2}=\frac{1}{4} \times \frac{22}{7} \times(3.5)^{2}$

$=\frac{1}{4} \times \frac{22}{7} \times 3.5 \times 3.5$

$=9.625 \mathrm{~m}^{2}$

$\therefore$ Area of the remaining part $=300-(4 \times 9.625)=261.5 \mathrm{~m}^{2}$

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