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The circumference of a given circular park is $55$ m. It is surrounded by a path of uniform width $35$ cm. What is the area of the path?

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23.125 m^{2}

19.635 m^{2}

17.245 m^{2}

27.155 m^{2}

answer is B.

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Detailed Solution

Given, the circumference of a given circular park is

55

Circumference of a circle is

2 πr

\Rightarrow

2 πr = 55

\Rightarrow r = \frac{7}{2 \times 22} \times 55

\Rightarrow

= \frac{35}{4}

m
Area of a circle is

π r^{2}

\Rightarrow

Area of this field =

π \times r^{2}

\Rightarrow

Area of this field

= π \times {(\frac{35}{4})}^{2}

\Rightarrow

Area of this field

= 240.625 m^{2}

A uniform width path is there in surrounding this circular field.
Width

= 0.35

m
Radius increased by

0.35

m
Now new radius will be

R = 0.35 + \frac{35}{4}

\Rightarrow

= \frac{910}{100}

cm
New Area

= π \times {(\frac{910}{100})}^{2}

\Rightarrow

New Area

= 260.26 m^{2}

Area of extended path

A = 260.26 - 240.625

\Rightarrow A = 19.635 m^{2}

Hence, the required area is

19.635 m^{2}

.
Hence, option 2 is correct.

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