the inner circumference of a circular track is 176 metre the track is 7 metre wide calculate the area of the track( b)cost of putting up a fence along the outer circle at the rate of rate 12 per metre
Answers
Answer:
}
• According to the Question Now :
\implies \tt Inner \:Circumference = 2\pi r⟹InnerCircumference=2πr
\implies \tt 176 = 2 \times \dfrac{22}{7} \times r⟹176=2×
7
22
×r
\implies \tt \cancel{176}\times \dfrac{7}{ \cancel{44}} = r⟹
176
×
44
7
=r
\implies \tt 4 \times 7 = r⟹4×7=r
\implies \blue{\tt r = 28m}⟹r=28m
\rule{300}{1}
⇒ Radius ( R ) = Radius ( r ) + Width
⇒ Radius ( R ) = 28 m + 7 m
⇒ Radius ( R ) = 35 m
\rule{300}{1}
(a) Area of the Track :
\longrightarrow \tt Area \:of \:Track = Outer \:Area - Inner \: Area⟶AreaofTrack=OuterArea−InnerArea
\longrightarrow \tt Area \:of \:Track = \pi {(R)}^{2} - \pi {(r)}^{2}⟶AreaofTrack=π(R)
2
−π(r)
2
\longrightarrow \tt Area \:of \:Track = \pi( {(R)}^{2} - {(r)}^{2} )⟶AreaofTrack=π((R)
2
−(r)
2
)
\longrightarrow \tt Area \:of \:Track = \dfrac{22}{7} ( {(35)}^{2} - {(28)}^{2} )⟶AreaofTrack=
7
22
((35)
2
−(28)
2
)
\longrightarrow \tt Area \:of \:Track = \dfrac{22}{7}(35 + 28)(35 - 28)⟶AreaofTrack=
7
22
(35+28)(35−28)
\longrightarrow \tt Area \:of \:Track = \dfrac{22}{\cancel7} \times 63 \times \cancel7⟶AreaofTrack=
7
22
×63×
7
\longrightarrow \tt Area \:of \:Track = 22 \times 63⟶AreaofTrack=22×63
\longrightarrow\large\boxed{\tt Area \:of \:Track = 1386 {m}^{2}}⟶
AreaofTrack=1386m
2
⠀
∴ Hence, Area of the Track is 1386 m².
\rule{300}{2}
(b) Cost of putting a fence along the outer circle @ Rs. 12 per Metre.
\longrightarrow \tt Cost = Circumference \times Rate⟶Cost=Circumference×Rate
\longrightarrow \tt Cost = 2\pi R \times Rate⟶Cost=2πR×Rate
\longrightarrow \tt Cost = (2 \times \dfrac{22}{ \cancel7} \times \cancel35) \times Rs. 12⟶Cost=(2×
7
22
×
3
5)×Rs.12
\longrightarrow \tt Cost = (2 \times 22\times 5)\times Rs.12⟶Cost=(2×22×5)×Rs.12
\longrightarrow\tt Cost = 220 \times Rs.12⟶Cost=220×Rs.12
\longrightarrow \large \boxed{\tt Cost = Rs. \: 2640}⟶
Cost=Rs.2640
⠀
∴ Cost of Outer Fencing is Rs. 2640.