Question

13. A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular
path is 44 m, find the inner circumference of the circular path. Also, find area of the path.
​

Answer 1

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Question}}}}$

A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also, find area of the path.

⠀⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

Given:

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• The circular pond is surrounded by a 2 m wide circular path.

• The outer circumference of circular path is 44 m

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To find:

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• find the inner circumference of the circular path.

• Also, find area of the path.

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Solution:

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Let the inner radius of the path is ' r '

As the circular path is 2 m wide.

So, the outer radius of the path is (r + 2)

.°. The outer circumference = 2π (r + 2)

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According to the question ,

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⠀⠀⠀⠀⠀$\sf{:\implies 2π(r+2)=44}$

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⠀⠀⠀⠀⠀$\sf{:\implies 2×\dfrac{22}{7}(r+2)=44}$

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⠀⠀⠀⠀⠀$\sf{:\implies (r+2)=\dfrac{7}{22}×\dfrac{1}{2}×44}$

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⠀⠀⠀⠀⠀$\sf{:\implies (r+2)=7}$

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⠀⠀⠀⠀⠀$\sf{:\implies r=7-2}$

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⠀⠀⠀⠀⠀⠀$\boxed{\bf{\pink{:⟹\:r\:=\:5}}}$

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NOW,

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The inner circumference of the path is

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⠀⠀⠀⠀⠀$\sf{:\implies 2πr}$

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⠀⠀⠀⠀⠀$\sf{:\implies 2×\dfrac{22}{7}×5\:m}$

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⠀⠀⠀⠀⠀$\sf{:\implies \dfrac{220}{7}\:m}$

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⠀⠀⠀⠀⠀$\sf{:\implies 31.43\:m}$

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Therefore,

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$\dashrightarrow\:\:\underline{\boxed{\sf the\:inner\:circumference\:of\:the\:path=31.43\:m}}$

Now,

Area of the circular path is

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⠀⠀⠀⠀⠀$\sf{:\implies π(r+2)^{2}-πr^{2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies \dfrac{22}{7}×[(5+2)^{2}-5^{2}]m^{2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies \dfrac{22}{7}×[49-25]\:m^{2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies \dfrac{22}{7}×24\:m^{2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies \dfrac{24×22}{7}\:m^{2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies {\cancel{\dfrac{528}{7}}}\:m^{2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies 75.43\:m^{2}......(approx)}$

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Hence,

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$\dashrightarrow\:\:\underline{\boxed{\sf area\:of\:the\:circular\:path\:=\:75.43\:m^{2}.....(approx)}}$

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