Question

i) Find the area of a circular pond that has a diameter of 12m.
ii)The pond is surrounded by a path of width 2m. If the costs $55 per square meter to pave the path with tiles, find the cost incurred.

Give step by step explanation please.​
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Answer 1

$\underbrace{ \huge \sf answer - 1st}$

$\blacksquare \: \red{ \bf{given : }}$

$\pmb{ \frak{\bigstar\: diametre = 12 \: m}}$

$\blacksquare \: \red{ \bf{find :}}$

$\pmb{ \frak {\bigstar \: area}}$

$\circ \: \underline{ \fbox{ \color{red}\: formulaes \: to \: be \: used :} } \: \downarrow$

$\underline{ \underline{ \bullet \pink{\pmb{ \: area \: of \: circle = \pi \: r ^{2} }}}}$

$\underline{ \underline{ \bullet \: \purple{\pmb{ \: radius = \frac{diameter}{2} }}}}$

$\underline{ \sf \: solution} : \longmapsto \: = \frac{22}{7} \times 6 \times 6 \\ = \frac{22}{7} \times 36 \\ \fbox{= 113.14}$

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$\underbrace {\huge \sf \: answer - 2nd}$

$\leadsto \pmb{ \frak{according \: to \: question : }}$

$\underline{ \underline \bold{ \blacktriangleright \color{gold} \: pond \: is \: surrounded \: by \: a \: path \: of \: width\: 2 \: m}}$

$\underline{ \underline \pink{ \bold{area \: of \: path = \pi \: ( {8}^{2} - {6}^{2} )}}}$

$\underline{ \sf \: solution}: \longmapsto = \frac{22}{7} \times 64 - 36 \\ = \frac{22}{7} \times 28 \\ = 22 \times 4 = 88$

$\bold{ \blacksquare \green{ \: cost \: per \: square \: metre =55}}$

$88 \times 55 \: \fbox{ = \ 4840}$

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Answer 2

$\sf\small\underline\green{Given:-}$

$\sf{\longrightarrow Diameter\:_{(circular\:pond)}=12m}$

$\sf{\longrightarrow Surrounded\:by\:_{(circular\:pond)}=2m}$

$\sf{\longrightarrow Paving\:cost\:_{(circular\:path)}=\ 55\:m^2}$

$\sf\small\underline\green{To\: Find:-}$

$\sf{\longrightarrow The\:cost\: incurred\:_{(for\:path)}=?}$

$\sf\small\underline\green{Solution:-}$

To solve this question at, first we have to find the radius of circular pond. Then calculate it's area as you noticed in the given question that this circular pond is surrounded by a path with 2m wide. It means here two circle is formed. One is outer circle with the radius of inner circle joint. Other is outer circle with diameter of 12m. Here we assume the outer circle's radius be R and Inner circle's radius be r.

$\sf\small\underline{Calculation:-}$

$\sf{\longrightarrow Radius\:_{(inner\: circle)}=\dfrac{Diameter}{2}}$

$\sf{\longrightarrow Radius\:_{(inner\: circle)}=\dfrac{12}{2}=6m}$

$\sf{\longrightarrow Radius\:_{(outer\: circle)}=Radius\:_{(inner\: circle+wide\:of\:path)}}$

$\sf{\longrightarrow Radius\:_{(outer\: circle)}=6+2=8m}$

$\sf{\implies Area\:_{(pond)}=\pi\:r^2}$

$\tt{\implies Area\:_{(pond)}=\dfrac{22}{7}\times\:6^2}$

$\tt{\implies Area\:_{(pond)}=\dfrac{22*36}{7}}$

$\tt{\implies Area\:_{(pond)}=\dfrac{792}{7}}$

$\tt{\implies Area\:_{(pond)}=113.14m^2}$

• $\sf{Now\: calculate\:the\:area\:of\:path:-}$

$\sf{\longrightarrow Area\:_{(path)}=Area\:_{(outer\: circle)}-Area\:_{(inner\:circle)}}$

$\rm{\longrightarrow Area\:_{(path)}=\pi\:R^{2}-\pi\:r^2}$

$\rm{\longrightarrow Area\:_{(path)}=\pi(R^2-r^2)}$

$\rm{\longrightarrow Area\:_{(path)}=\pi(8^2-6^2)}$

$\rm{\longrightarrow Area\:_{(path)}=\pi(64-36)}$

$\rm{\longrightarrow Area\:_{(path)}=28\pi}$

$\rm{\longrightarrow Area\:_{(path)}=\dfrac{22}{7}\times\:28}$

$\rm{\longrightarrow Area\:_{(path)}=22\times\:4}$

$\rm{\longrightarrow Area\:_{(path)}=88\:m^2}$

• $\sf{Now\: calculate\: paving\:cost\:of\:path:-}$

$\sf{\longrightarrow Paving\:cost=Area\:_{(path)}\times\:rate}$

$\sf{\longrightarrow Paving\:cost=88\times\:55}$

$\sf{\longrightarrow Paving\:cost=\ 4840}$

$\sf\large{Hence,}$

$\tt{\longrightarrow The\:cost\: incurred\:_{(for\:path)}=\ 4840}$