Question

6. A circular garden has a path running around it on its outside. The garden has a circumference of 396 m
and the path is 3.5 m wide. Find the area of the path​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Circular garden has a path running around it on its outside

$\:\:$

• Garden has a circumference of 396 m

$\:\:$

• Path is 3.5 m wide

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Area of the path

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let "r" be the radius of circular garden

$\:\:$

$\underline{\bold{\texttt{Circumference of circle :}}}$

$\:\:$

➠ 2πr

$\:\:$

Given that, garden has a circumference of 396 m

$\:\:$

So,

$\:\:$

➜ 2πr = 396

$\:\:$

➜ πr = $\sf \dfrac { 396 } { 2 }$

$\:\:$

➜ πr = 198

$\:\:$

➜ r = 198 ÷ π

$\:\:$

➜ $\sf r = 198 ÷ \dfrac { 22 } { 7 }$

$\:\:$

➜ $\sf r = 198 \times \dfrac { 7 } { 22 }$

$\:\:$

➜ $\sf r = 9 \times 7$

$\:\:$

➨ r = 63 m

$\:\:$

$\underline{\bold{\texttt{Area of circle :}}}$

$\:\:$

➠ πr²

$\:\:$

$\underline{\bold{\texttt{Area of circular garden :}}}$

$\:\:$

➜ $\sf \dfrac { 22 } { \cancel 7 } \times \cancel {63} \times 63$

$\:\:$

➜ $\sf 22 \times 9 \times 63$

$\:\:$

➨ 12474 sq. m

$\:\:$

$\underline{\bold{\texttt{Radius of garden along with the path :}}}$

$\:\:$

➠ R = 63 + 3.5 = 66.5 m

$\:\:$

$\underline{\bold{\texttt{Area of garden along with the path :}}}$

$\:\:$

➠ πR²

$\:\:$

➜ $\sf \dfrac { 22 } { \cancel 7 } \times \cancel {66.5} \times 66.5$

$\:\:$

➜ $\sf 22 \times 9.5 \times 66.5$

$\:\:$

➨ 13898.5 sq. m

$\:\:$

$\underline{\bold{\texttt{Area of path -}}}$

$\:\:$

Area of garden ⠀⠀⠀− ⠀ ⠀Area of garden

along with the path ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\:\:$

➜ Area of path = 13898.5 - 12474

$\:\:$

➜ Area of path = 1424.5 sq. m

$\:\:$

• Hence the path running around garden has an area of 1424.5 sq. m

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Circular garden has a path running around it on its outside

$\:\:$

• Garden has a circumference of 396 m

$\:\:$

• Path is 3.5 m wide

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Area of the path

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let "r" be the radius of circular garden

$\:\:$

$\underline{\bold{\texttt{Circumference of circle :}}}$

$\:\:$

➠ 2πr

$\:\:$

Given that, garden has a circumference of 396 m

$\:\:$

So,

$\:\:$

➜ 2πr = 396

$\:\:$

➜ πr = $\sf \dfrac { 396 } { 2 }$

$\:\:$

➜ πr = 198

$\:\:$

➜ r = 198 ÷ π

$\:\:$

➜ $\sf r = 198 ÷ \dfrac { 22 } { 7 }$

$\:\:$

➜ $\sf r = 198 \times \dfrac { 7 } { 22 }$

$\:\:$

➜ $\sf r = 9 \times 7$

$\:\:$

➨ r = 63 m

$\:\:$

$\underline{\bold{\texttt{Area of circle :}}}$

$\:\:$

➠ πr²

$\:\:$

$\underline{\bold{\texttt{Area of circular garden :}}}$

$\:\:$

➜ $\sf \dfrac { 22 } { \cancel 7 } \times \cancel {63} \times 63$

$\:\:$

➜ $\sf 22 \times 9 \times 63$

$\:\:$

➨ 12474 sq. m

$\:\:$

$\underline{\bold{\texttt{Radius of garden along with the path :}}}$

$\:\:$

➠ R = 63 + 3.5 = 66.5 m

$\:\:$

$\underline{\bold{\texttt{Area of garden along with the path :}}}$

$\:\:$

➠ πR²

$\:\:$

➜ $\sf \dfrac { 22 } { \cancel 7 } \times \cancel {66.5} \times 66.5$

$\:\:$

➜ $\sf 22 \times 9.5 \times 66.5$

$\:\:$

➨ 13898.5 sq. m

$\:\:$

$\underline{\bold{\texttt{Area of path -}}}$

$\:\:$

Area of garden ⠀⠀⠀− ⠀ ⠀Area of garden

along with the path ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\:\:$

➜ Area of path = 13898.5 - 12474

$\:\:$

➜ Area of path = 1424.5 sq. m

$\:\:$

• Hence the path running around garden has an area of 1424.5 sq. m