Question

The diameter of circular lawn is 84 meter and path of 7 m wide runs round inside the lawn,find the cost of paving the lawn with stones at RS.15 per square meter

Answer 1

AnswEr :

$\bullet\:\textsf{Diameter of Circular Lawn (d) = 84 m}\\\bullet\:\textsf{Radius of Circular Lawn (R) = 42 m}\\\bullet\:\textsf{Path runs round Inside the Lawn (w) = 7 m}\\\bullet\:\textsf{Radius of Lawn excluding Path = (R - w) = (42 - 7) = 35 m}$

$\rule{100}{2}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies \texttt{Area of Path = (Outer Area - Inner Area) of Lawn}\\\\\\:\implies\texttt{Area of Path = \sf(\pi {R}^{2}) -(\pi{r}^{2} })\\\\\\: \implies\texttt{Area of Path = \sf\pi ({R}^{2} -{r}^{2}) }\\\\\\: \implies\texttt{Area of Path = \sf \dfrac{22}{7} \times({(42m)}^{2} -{(35m)}^{2}) }\\\\ \scriptsize \qquad{\bf{ \dag}\quad( {a}^{2} - {b}^{2}) = (a + b)(a - b)}\\\\: \implies\texttt{Area of Path = \sf \dfrac{22}{7} \times(42m + 35m) \times (42m - 35m) }\\\\\\: \implies\texttt{Area of Path = \sf \dfrac{22}{\cancel7} \times77m \times \cancel7m } \\\\\\: \implies\texttt{Area of Path = \sf 22 \times 77{m}^{2} } \\ \\ \\: \implies\texttt{Area of Path = \sf 1694 \:{m}^{2} }$

$\rule{250}{1}$

$\underline{\bigstar\:\textsf{Cost of Paving of Lawn :}}$

$\longrightarrow \texttt{Cost of Paving = Area of Path \times Rate} \\\\\\\longrightarrow \tt Cost \: of \:Paving =1694 \: \cancel{{m}^{2}} \times Rs. \: 15 \:\cancel{{m}^{ - 2}} \\ \\ \\\longrightarrow \tt Cost \: of \:Paving =1694 \times Rs. \: 15 \\ \\ \\\longrightarrow \boxed{\red{\tt Cost \: of \:Paving =Rs. \:25410}}$

⠀

$\therefore\underline{\textsf{Cost of Paving of lawn path is {\textbf{Rs. \:25410}}}}$

Answer 2

Answer:

Outer Radius of the path , R = 42m

Width of the path = 7m

Inner radius of the path , r = 42 - 7 = 35m

Area of the path = ar of outer circle - ar of the inner circle

= pie R² - pie r²

= 22/7 × (42)sq - 22/7 × (35) sq

= 22/7 × 1764 - 22/7 × 1225

= 22/7 ( 1764 - 1225 )

= 22/7 × 539

= 1694 m²

Price @ Rs 15 / m²

= Rs 1694 × 15

= Rs 25410