એક વર્તુળાકાર તળાવનો વ્યાસ 17.5 મી છે. તેની બ | vedclass

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Question

Given that, a circular pond is surrounded by a wide path.

The diameter of circular pond $=17.5 \,m$

$	herefore \quad$ Radius of circular pond $

Vedclass · Accepted Answer

$3061.50$

Vedclass · Answer

Given that, a circular pond is surrounded by a wide path.

The diameter of circular pond $=17.5 \,m$

$	herefore \quad$ Radius of circular pond $\left(r_{i}ight)=\frac{	ext { Diameter }}{2}$

i.e., $\quad O A=r_{i}=\frac{17.5}{2}=875 \, m$

and the width of the path $=2 \,m$

$i, e$ $A B=2 \,m$

Now, $\quad$ length of $O B=O A+A B=r_{i}+A B$

Let $\quad(r_e)=8.75+2=10.75\, m$

So, area of circular path $=$ Area of outer circle i.e., (circular pond $+$ path) $-$ Area of circular pond

$=\pi r_{e}^{2}-\pi r_{i}^{2}$

$=\pi\left(r_{e}^{2}-r_{i}^{2}ight)$

$=\pi\left\{(10.75)^{2}-(8.75)^{2}ight\}$

$=\pi\{(10.75+8.75)(10.75-8.75)\}$

$=3.14 	imes 19.5 	imes 2$

$=122.46 \,m ^{2}$

Now, cost of constructing the path per square metre $=Rs.\, 25$

$	herefore$ cost constructing the path $Rs.\, 122.46 \,m ^{2}=122.46 	imes 25$

$=Rs.\, 3061.50$

Hence, required cost of constructing the path at the rate of $Rs.\, 25$ per $m ^{2}$ is $Rs.\, 3061.50 .$

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