Question

the inner circumference of a circular track is 176 the track is 7 metre wide calculate the: (a) area of the track. (b)cost of putting a persons along the outer circle @ rupees 12 per metre used equal to 22 /7​

Answer 1

Correct Question :

The inner circumference of a circular track is 176 m². The track is 7 m wide.

Calculate the : (a) Area of the Track. (b) Cost of putting a fence along the outer circle @ Rs. 12 per Metre. Use π equal to 22 /7.

AnswEr :

$\bold{Given} \begin{cases}\sf{Inner \:Circumference=176 {m}^{2} } \\ \sf{Width=7m}\end{cases}$

$\begin{center}\setlength{\unitlength}{1.3 pt}\begin{picture}(100,100)(0,0)\put(0,0){\circle{50}} \put(0,0){\circle{22}} \put(0,0){\circle*{1.5}}\put(-16,0){\line(1,0){31.5}}\put(-15,1.5){ 7 }\end{picture}\setlength{\unitlength}{1 pt}\end{center}$

• According to the Question Now :

$\implies \tt Inner \:Circumference = 2\pi r$

$\implies \tt 176 = 2 \times \dfrac{22}{7} \times r$

$\implies \tt \cancel{176}\times \dfrac{7}{ \cancel{44}} = r$

$\implies \tt 4 \times 7 = r$

$\implies \blue{\tt r = 28m}$

$\rule{300}{1}$

⇒ Radius ( R ) = Radius ( r ) + Width

⇒ Radius ( R ) = 28 m + 7 m

⇒ Radius ( R ) = 35 m

$\rule{300}{1}$

(a) Area of the Track :

$\longrightarrow \tt Area \:of \:Track = Outer \:Area - Inner \: Area$

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

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

$\longrightarrow \tt Area \:of \:Track = \dfrac{22}{7} ( {(35)}^{2} - {(28)}^{2} )$

$\longrightarrow \tt Area \:of \:Track = \dfrac{22}{7}(35 + 28)(35 - 28)$

$\longrightarrow \tt Area \:of \:Track = \dfrac{22}{\cancel7} \times 63 \times \cancel7$

$\longrightarrow \tt Area \:of \:Track = 22 \times 63$

$\longrightarrow\large\boxed{\tt Area \:of \:Track = 1386 {m}^{2}}$

⠀

∴ 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.

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

$\longrightarrow \tt Cost = 2\pi R \times Rate$

$\longrightarrow \tt Cost = (2 \times \dfrac{22}{ \cancel7} \times \cancel35) \times Rs. 12$

$\longrightarrow \tt Cost = (2 \times 22\times 5)\times Rs.12$

$\longrightarrow\tt Cost = 220 \times Rs.12$

$\longrightarrow \large \boxed{\tt Cost = Rs. \: 2640}$

⠀

∴ Cost of Outer Fencing is Rs. 2640.

Answer 2

Answer:

Radius of inner circle = 176/2*7/22=28m

Radius of outer circle = 35m

Area of path= (22/7*35*35) - (22/7*28*28) ⠀⠀⠀⠀⠀⠀⠀ = 1386m^2

Total Cost = 2×22/7×35×12

⠀⠀⠀⠀⠀⠀⠀= 2640 rupees