Question

There is a circular lawn of radius 28 m. A path of 7 m width is laid around the lawn.
What will be the area of the path? ​

Answer 1

GIVEN:-

• Radius :- 28 cm
• Width :- 7 m

TO FIND:-

• Area of path

SOLUTION:-

[ The path is 7m wide. ]

The radius of the circular lawn is 28m.

★Then the area of the lawn is

→ π × 28^2m^2

→ 784π m^2

The radius of the lawn along with the path is (28 + 7)m = 35 m

★Then its area is

→ π × 35^2 m^2

→ 1225π m^2

Therefore the area of path is

→ area of the lawn along with path - area of the lawn

→ (1225π - 784π) m^2

→ 441π m^2

→ 441 × 22/7 m^2

→ 1386 m^2

━━━━━━━━━━━━━━━━━━━━

Answer 2

Figure

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(1.2,0)(1.121,1.121)(0,1.2)\qbezier(1.2,0)(1.121,-1.121)(0,-1.2)\qbezier(0,-1.2)(-1.121,-1.121)(-1.2,0)\qbezier(-1.2,0)(-1.121,1.121)(0,1.2)\put(-0,0){\vector(-1,0){2.3}}\put(0,0){\vector(0,1){1.2}}\put(-1.9,0.2){ \bf 35m }\put(0.2,0.3){ \bf 28m }\end{picture}$

Given

• Radius of the lawn (r) = 28m
• Radius of the whole circle (R) = 35m
• Width of the path = 7m

To find

• Area of the path.

Solution

$\sf\pink{⟶}$ This question will be solved in two parts.

→ In first part we have to find the area of the lawn.

→ In second part we have to find the area of the whole circle.

• Using the formula

$\large{\underline{\boxed{\tt{Area\: of\: a\: circle = πr^2}}}}$

★ Area of the lawn

$\tt:\implies\: \: \: \: \: \: \: \: {Area = \dfrac{22}{7} × (28)^2}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = \dfrac{22}{\not{7}} × \not{28} × 28}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 22 × 4 × 28}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 88 × 28}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 2,464m^2}$

⠀

★ Area of the whole circle

$\tt:\implies\: \: \: \: \: \: \: \: {Area = \dfrac{22}{7} × (35)^2}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = \dfrac{22}{\not{7}} × \not{35} × 35}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 22 × 5 × 35}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 110 × 35}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area = 3,850m^2}$

⠀

⟹ Area of the circular path

$\underline{\boxed{\sf{Area\: of\: whole\: circle - Area\: of\: lawn}}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area\: of\: path = 3,850 - 2,464}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {Area\: of\: path = 1,386m^2}$

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