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The cost of fencing a semi-circular garden of radius $14$ m at a rate of $₹ 10$ per metre is,

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₹ 1080

₹ 1020

₹ 700

₹ 720

answer is D.

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Detailed Solution

It is given that the radius of semi-circular garden is

14

m. The rate of fencing is

₹ 10

per metre.
We need to find the cost for fencing the garden.
We know that the circumference of a semi-circle is

π r

, where

r

is its radius.
The length to be fenced or the perimeter of the garden

= Circumference of semicircle + Diameter of semicircle

We know that,
Diameter,

d = 2 r

By data,

r = 14

\Rightarrow Perimeter = πr + 2 r

\Rightarrow Perimeter = (\frac{22}{7} \times 14) + (2 \times 14)

\Rightarrow Perimeter = 44 + 28

\Rightarrow Perimeter = 72

m
Therefore,

Cost = Perimeter \times Rate of fencing

\Rightarrow Cost = 72 \times ₹ 10

\Rightarrow Cost = ₹ 720

Therefore, the cost of fencing the semi-circular garden is

₹ 720

.
Hence, the correct option is 4.

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