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A path of width 3.5 m runs around a semicircular grassy plot whose perimeter is 72 m. Find the area of the path $(use π = \frac{22}{7})$

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173 m^{2}

173.25 m^{2}

203 m^{2}

203.25 m^{2}

answer is B.

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Detailed Solution

It is known that semi- circle of perimeter is,

= πr + 2 r

Given,
The grassy plot perimeter is 72 m.
We know that,

πr + 2 r = 72

\Rightarrow \frac{22}{7} r + 2 r = 72

\Rightarrow 22 r + 14 r = 504

\Rightarrow 36 r = 504

\Rightarrow r = \frac{504}{36}

\Rightarrow r = 14 m

Radius of Semi-circle plot,

r = 14 m

Here,
Semi-circle plot area,

= \frac{1}{2} π r^{2}

= \frac{1}{2} \times \frac{22}{7} \times (14)^{2}

= 308 m^{2}

It is given the path of width 3.5 m is add of the semi-circle plot.
Therefore,
So, radius become,

= r + 3.5

= 17.5 m

New semi-circle plot area

= \frac{1}{2} \times \frac{22}{7} \times (17.5)^{2}

= 481.25 m^{2}

Now, we have,
Area of path = New semi-circle plot area− Semi-circle plot area
Area of path

= 481.25 - 308

Area of path = 173.25 m^{2}

Thus, the value area of path

= 173.25 m^{2}

.
Option 2 is correct.

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