A circular pond is 17.5 ,m is of diameter. It | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $Rs.\, 3061.50 .$

A circular pond is $17.5 \,m$ is of diameter. It is surrounded by a $2 \,m$ wide path. Find the cost of constructing the path at the rate of $Rs.\, 25$ per $m ^{2}$ (in $Rs.$)

Similar Questions

Find the area of the shaded region in $Fig.$ where arcs drawn with centres $A , B , C$ and $D$ intersect in pairs at mid-points $P , Q , R$ and $S$ of the sides $AB , BC,$ $CD$ and $DA ,$ respectively of a square $ABCD$ (Use $\pi=3.14)$ (in $cm ^{2}$)

Find the area of the flower bed (with semi-circular ends) shown in $Fig.$

In $Fig.$ $AB$ is a diameter of the circle, $AC =6\, cm$ and $BC =8 \,cm .$ Find the area of the shaded region (Use $\pi=3.14$ ). (in $cm ^{2}$)

The circumference of a circular ground is $220\, m .$ Outside it, runs a road of equal width. If the circumference of the ground with the road is $264\, m$, find the width of the road. (in $m$)

The radius of a circular ground is $56\, m$. Inside it, runs a road of width $7 \,m$ all along its boundary. Find the area of this road. (in $m^2$)