Question

A circular path 7m wide surrounds a circular swimming pool of circumference 308m the cost of paving the path at rs 10 per sq m

Answer 1

AnswEr :

• Inner Circumference = 308 m
• Width of Path = 7 m
• Find the Cost of Paving the path at Rs. 10 @ metre²

• I N N E R ⠀R A D I U S ⠀O F ⠀P O O L :

$\longrightarrow \tt Inner \:Circumference= 2 \pi r \\ \\\longrightarrow \tt308m = 2\pi r \\ \\\longrightarrow \tt308m = 2 \times \dfrac{22}{7} \times r \\ \\\longrightarrow \tt\cancel{308m} \times \dfrac{7}{ \cancel{2 \times 22}} = r \\ \\\longrightarrow \tt7m \times 7 = r \\ \\\longrightarrow \blue{\tt r = 49 \:m}$

$\rule{300}{1}$

• O U T E R ⠀R A D I U S ⠀O F ⠀P O O L :

↠ Outer Radius = Inner Radius + Width

↠ R = 49 m + 7 m

↠ R = 56 m

$\rule{300}{2}$

• Cost of Paving of Path around Pool :

$\implies \tt Cost = Area \:of \:Path \times Rate \\ \\\implies \tt Cost = (\pi {R}^{2} - \pi {r}^{2})\times Rate \\ \\\implies \tt Cost = \pi({R}^{2} - {r}^{2})\times Rate \\ \\\implies \tt Cost = [\frac{22}{7} \times ({56}^{2} - {49}^{2})]\times 10 \\ \\\implies \tt Cost = [\frac{22}{7} \times (56 + 49)(56 - 49)]\times 10 \\ \\\implies \tt Cost = [\frac{22}{\cancel7} \times 105 \times\cancel7]\times 10 \\ \\\implies \tt Cost =22 \times 105 \times 10 \\ \\\implies\large\boxed{ \red{\tt Cost =Rs. \: 23100}}$

⠀

∴ Cost of Paving of Path will be Rs. 23100

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Answer 2

❏ Used Formula:-

✏For a circle with radius r ,

$\sf\longrightarrow\boxed{ Area=\pi r{}^{2}}$

$\sf\longrightarrow\boxed{Perimeter=2\pi r}$

✏For 2 concentric circles with radius R and r,

where, R>r.

$\sf\longrightarrow\boxed{ Area_{\red{ring}}=\pi \times(R{}^{2}-r{}^{2})}$

❏ Question:-

Q) A circular path 7m wide surrounds a circular swimming pool of circumference 308m the cost of paving the path at rs 10 per sq m.

❏ Solution:-

❚➾ :Given:

• width of circular path= 7 m.

• circumference of the pool= 308 m.

❚➾ :To Find:

•cost of paving the path at rs 10 per m² .

❚❚➾ANS:-

Let, the radius of the pool is = r metre.

Now according to the Question circumference of the pool is = 308 m

$\sf\therefore 2\times \pi times r= 308$

$\sf\longrightarrow 2\times \frac{22}{7}\times r=308$

$\sf\longrightarrow r=\frac{\cancel{308}\times 7}{\cancel{22}\times\cancel2}$

$\sf\longrightarrow r=7\times7$

$\sf\longrightarrow \boxed{\red{r=49\:metre}}$

$\bf\therefore$ radius of the pool with the circular path = (49+7) m= 56 m.

➾ Hence, Area of the pool,,

$\sf\therefore A_{\red{pool}}=\pi\times 49{}^{2}$

➾ Hence, Area of the pool with circular path.

$\sf\therefore A_{\red{pool+path}}=\pi\times 56{}^{2}$

➾ Hence, Area of the circular path.

$\sf\therefore A_{\red{path}}=\pi\times 56{}^{2}-\pi\times 49{}^{2}$

$\bf\therefore A_{\red{path}}=\pi\times( 56{}^{2}- 49{}^{2})$

$\sf\therefore A_{\red{path}}=\frac{22}{7}\times( 56- 49)\times(56+49)$

$\sf\therefore A_{\red{path}}=\frac{22}{\cancel7}\times\cancel7\times105$

$\sf\therefore A_{\red{path}}=22\times 105\:m{}^{2}$

$\sf\therefore\boxed{A_{\red{path}}=2310\:m{}^{2}}$

$\therefore$ cost of paving the path at rs 10 per m² is.

$\sf\longrightarrow Cost=(10\times 2310)\:Rs$

$\sf\longrightarrow\boxed{\red{\bf Cost=23,100\:Rs}}$

∴ Cost of paving the path is = 23,100 Rs.

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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