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If a well of diameter $150 cm$ has a $30 cm$ wide parapet running around it, then what would be the area of the parapet?

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16971.428

{cm}^{2}

1697.142

{cm}^{2}

169.714

{cm}^{2}

16971.42

{cm}^{2}

answer is A.

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Detailed Solution

We have been given,
Diameter of well

= 150 cm

Width of parapet = 30 cm
Radius of well will be

r = \frac{d}{2}

.
Substituting the values,

\Rightarrow \frac{150}{2}

\Rightarrow 75 cm

Now, as a parapet of the well it forms two circles.
One will be the inner circle and the second will be the outer circle.
As radius is half of the diameter, therefore, the radius of inner circle

(r) = 75 cm

.
Radius of outer circle

R

=Inner radius + Width of parapet
Question Image

Substituting the values,

\Rightarrow 75 + 30

\Rightarrow 105 cm

Now, calculating the area of the parapet,
Area of parapet

=

Area of outer circle

-

Area of inner circle
Substituting the values,

\Rightarrow π R^{2} - π r^{2} = π (R^{2} - r^{2})

\Rightarrow \frac{22}{7} [(105)^{2} - (75)^{2}]

= \frac{22}{7} \times 5400

\Rightarrow \frac{118800}{7}

\Rightarrow 16971.428 {cm}^{2}

Therefore, the required value is 16971.428cm2.
Hence, option 1 is correct.

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