Question

outer circumference of a circular Park is 396 there is a path inside the park whose width is 3.5 All Around The Park find the area of the path also find the cost of gravelling the path @ rupees 4.15 per metre square ​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{Outer\: Circumference=396 \:{m}^{2} }\\\sf{Width=3.5m}\\ \sf{Cost \:of \:Gravelling = Rs. \:4.15 \:@metre}\\\sf{Find \:the \:Cost \:of \:Gravelling \:the \:Path.} \end{cases}$

⋆ Refrence of Image is in the Diagram :

$\begin{center}\setlength{\unitlength}{1.3 pt}\begin{picture}(100,100)(0,0)\put(0,0){\circle{50}} \put(0,0){\circle{22}} \put(0,0){\circle*{1.5}}\put(-16,0){\line(1,0){31.5}}\put(-15,1.5){\tiny 3.5 m }\end{picture}\setlength{\unitlength}{1 pt}\end{center}$

• Calculation of Outer Radius of Park :

$\longrightarrow\tt Outer\: Circumference= 2\pi R \\ \\\longrightarrow\tt 396= 2 \times\dfrac{22}{7} \times R \\ \\\longrightarrow\tt \cancel{396} \times\dfrac{7}{ \cancel{2 \times 22}} = R \\ \\\longrightarrow\tt9 \times 7 = R \\ \\\longrightarrow \blue{\tt R = 63\:m}$

$\rule{300}{1}$

• I N N E R ⠀R A D I U S :

↠ Inner Radius = Outer Radius – Width

↠ r = R – width

↠ r = (63 – 3.5) m

↠ r = 59.5 m

$\rule{300}{1}$

• Calculation of Area of the Path :

$\implies \tt Area\:of\:Path = Outer \:Area - Inner \:Area \\ \\\implies \tt Area\:of\:Path =\pi {(R)}^{2} - \pi {(r)}^{2} \\ \\\implies \tt Area\:of\:Path =\pi ({(R)}^{2} - {(r)}^{2}) \\ \\\implies \tt Area\:of\:Path =\pi({(63)}^{2} - {(59.5)}^{2}) \\ \\\implies \tt Area\:of\:Path =\pi(63 - 59.5)(63 + 59.5) \\ \\\implies \tt Area\:of\:Path = \dfrac{22}{\cancel7} \times \cancel{3.5} \times 122.5 \\ \\\implies \tt Area\:of\:Path =22 \times 0.5 \times 122.5 \\ \\\implies \boxed{ \red{\tt Area\:of\:Path =1347.5 \:{m}^{2} }}$

$\rule{300}{2}$

• Calculation of Cost of Gravelling :

$\implies \tt Cost = Area \:of \:Path \times Rate \\ \\\implies \tt Cost = 1347.5 \times 4.15 \\ \\\implies \tt Cost = Rs.\: 5592.125 \\ \\\implies\boxed{ \red{\tt Cost\approx Rs.\: 5592}}$

⠀

∴ Cost of Gravelling of Park is Rs. 5592

#answerwithquality #BAL

Answer 2

Answer:

$\bold\red{Area\:of\:path=1347.5{m}^{2}}$

$\bold\red{Cost=Rs.5592}$

__________________________

$\textbf{\underline{Given\::}}$

• Outer circumference = 396 m
• Width of path = 3.5 m
• Rate of gravelling = 4.15 sq.m
• Area of path and cost of gravelling

$\textbf{\underline{\underline{Solution\::}}}$

● Outer circumference= 396 m

$\longrightarrow\tt 2\pi r = 396\:m$

$\longrightarrow\tt 2\times 3.1416 \times r =396\:m$

$\longrightarrow\tt 6.2832\times r =396\:m$

$\longrightarrow\tt r =\frac{396}{6.2832}\:m$

$\longrightarrow\tt r = 63\:m$

________________________

Inner radius = Outer radius- Width

$\longrightarrow\tt R = (63-3.5)\:m$

$\longrightarrow\tt R = 59.5\:m$

________________________

$\longrightarrow\tt Area\: of\: path = Outer\: area - Inner \:area$

$\longrightarrow\tt Area\: of\: path =\pi {r}^{2}- \pi {R}^{2}$

$\longrightarrow\tt Area\: of\: path =(3.1416\times{63}^{2} - 3.1416 \times {59.5}^{2}) {m}^{2}$

$\longrightarrow\tt Area\: of\: path = (12469.0104- 11122.05){m}^{2}$

$\longrightarrow\tt Area\: of\: path = 1347.5\:{m}^{2}$

_________________________

$\longrightarrow\tt Cost = Rate\times Area$

$\longrightarrow\tt Cost =Rs. 4.15\times 1347.5$

$\longrightarrow\tt Cost= Rs.5592.125$

$\longrightarrow\tt Cost =Rs.5592$

#Answerwithquality

#BAL