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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.
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Solution
It is given that the length of the rectangular piece is 20 m and its width is 15 m .
And, from each corner a quadrant each of radius 3 . 5 m has been cut out .
A rough figure for this is given below:
∴ Area of the remaining part = Area of the rectangular piece - (4 x Area of a quadrant of radius 3 . 5m)
Now, area of the rectangular piece = \[20 \times 15 = 300 m^2 \]
And, area of a quadrant with radius \[3 . 5 m =\frac{1}{4} \pi r^2 = \frac{1}{4} \times \frac{22}{7} \times (3 . 5 )^2 \]
\[ = \frac{1}{4} \times \frac{22}{7} \times 3 . 5 \times 3 . 5\]
\[ = 9 . 625 m^2 \]
∴ Area of the remaining part = \[ 300 - (4 \times 9 . 625) = 261 . 5 m^2\]
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