A square water tank has its side equal to $ 40 \mathrm{~m} $. There are four semi-circular grassy plots all round it. Find the cost of turfing the plot at $ ₹ 1.25 $ per square metre (Take $ \pi=3.14) $.

Given: 

A calf is tied with a rope of length \( 6 \mathrm{~m} \) at the corner of a square grassy lawn of side \( 20 \mathrm{~m} \).

The length of the rope is increased by \( 5.5 \mathrm{~m} \).

To do: 

We have to find the increase in area of the grassy lawn in which the calf can graze.

Solution:

Side of the square water tank $= 40\ m$

Radius of each semi-circular grassy plot $=\frac{40}{2}\ m=20\ m$

Rate of turfing the plot per $\mathrm{m}^{2}=Rs.\ 1.25$ 

Area of a semi-circular plot of radius $r$ is $\frac{1}{2} \pi r^{2}$.

Therefore,

Area of four semicircular plots around the square $=4 \times \frac{1}{2} \pi r^{2}$

$=2 \times 3.14 \times(20)^{2} \mathrm{~m}^{2}$

$=2 \times 3.14 \times 400 \mathrm{~m}^{2}$

$=800 \times 3.14 \mathrm{~m}^{2}$

$=2512 \mathrm{~m}^{2}$
Total cost of turfing $=Rs.\ 2512 \times 1.25$

$=Rs.\ 3140$

The cost of turfing the plot is Rs. 3140.

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Updated on: 10-Oct-2022

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