Question
A $4.2\ m$ wide road surrounds a circular plot whose circumference is $176\ m.$ Find the cost of paving the road at $Rs.75$ per $m^2.$
✓
Answer
We know,
The area of the ring between two concentric circles equals the area of the larger circle minus the area of smaller circle.
Let the radius of the outer and inner ring be $R$ and $r$ respectively.
Here the circular garden is the inner circle and the $7\ m$ wide road is the ring
The Circumference of a Circle with radius $r=2 \pi r$
Here,
$2 \pi r=176$
$\Rightarrow r=\frac{176}{2 \pi}$
$=\frac{176 \times 7}{2 \times 22}$
$=28$
$\Rightarrow r=28\ m$
$\Rightarrow R=28+4.2$
$=32.2\ m $
inner Circle has radius $r$
$=28 m$ and outer Circle has radius $R$
$=32.2\ m$
$ \pi\left(32.2^2-28^2\right)$
$=\frac{22}{7} \times(1036.84-784)$
$=\frac{22}{7} \times 252.84 $
$=794.64\ m ^2$
The cost of paving the road at the rate of $Rs. 150$ per $m ^2$
$=794.64 \times 75$
$=\text { Rs. } 59,598 .$
The area of the ring between two concentric circles equals the area of the larger circle minus the area of smaller circle.
Let the radius of the outer and inner ring be $R$ and $r$ respectively.
Here the circular garden is the inner circle and the $7\ m$ wide road is the ring
The Circumference of a Circle with radius $r=2 \pi r$
Here,
$2 \pi r=176$
$\Rightarrow r=\frac{176}{2 \pi}$
$=\frac{176 \times 7}{2 \times 22}$
$=28$
$\Rightarrow r=28\ m$
$\Rightarrow R=28+4.2$
$=32.2\ m $
inner Circle has radius $r$
$=28 m$ and outer Circle has radius $R$
$=32.2\ m$
$ \pi\left(32.2^2-28^2\right)$
$=\frac{22}{7} \times(1036.84-784)$
$=\frac{22}{7} \times 252.84 $
$=794.64\ m ^2$
The cost of paving the road at the rate of $Rs. 150$ per $m ^2$
$=794.64 \times 75$
$=\text { Rs. } 59,598 .$
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