A path of 4 m width runs round a semi­circular grassy plot whose circumference is $163\frac{3}{7}\ m$. Find the cost of gravelling the path at the rate of Rs. 1.50 per square metre.

Given:

A path of 4 m width runs round a semi­circular grassy plot whose circumference is $163\frac{3}{7}\ m$.

To do:

We have to find the cost of gravelling the path at the rate of Rs. 1.50 per square metre.

Solution:

Width of the path around the semicircular grassy plot $= 4\ m$.

Circumference of the plot $= 81\frac{5}{7}\ m$

$=\frac{572}{7}\ m$

Let $r$ be the radius of the plot. 

This implies,

$\frac{2\pi r}{2}=\frac{572}{7}$

$\Rightarrow \frac{22}{7} r=\frac{572}{7}$

$\Rightarrow r=\frac{572}{7} \times \frac{7}{22}$

$\Rightarrow r=26$

The radius of the plot is $26 \mathrm{~m}$.

Width of the path $=4 \mathrm{~m}$

Outer radius $R=26+4=30 \mathrm{~m}$

Cost of gravelling at the rate of Rs. 1.50 per $\mathrm{m}^{2}=Rs.\ 352 \times \frac{150}{100}$

$=Rs.\ \frac{352 \times 3}{2}$

$=Rs.\ 176 \times 3$

$=Rs.\ 528$

The  cost of gravelling the path at the rate of Rs. 1.50 per square metre is Rs. 528.

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Updated on: 10-Oct-2022

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