Question

A circular path has to be constructed around a circular lawn. if the outer and inner circumferences of the path are 88 cm and 44 cm respectively, find the width and area of the path.​

Answer 1

Width of the path is 7 cm, and Area of the circular path is 462 cm²

Let the radius of inner circle be r

Given, Circumference of inner circle = 44 cm.

∴ C = 44 cm

⇒ C = 44

⇒ 2πr = 44

⇒ πr = 22

⇒r = 7 cm.

Now, Let the radius of outer circle be R

Given, Circumference of inner circle = 88 cm.

∴ C = 88 cm

⇒ C = 88

⇒ 2πR = 88

⇒ πR= 44

⇒ R= 14 cm.

Width of the path = R - r = 14 - 7 = 7cm.

Area of inner circle

⇒a = πr²

⇒a = π(7)²

⇒a = 49π

Area of Outer circle

⇒A = πR²

⇒A = π(14)²

⇒A = 196 π

Area of the Path

= A - a

= (196 - 49) π

= 147 π

= 147 ( 22) / 7

= 21 ( 22)

= 462 cm²

Therefore, Area of the path is 462 cm².

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Answer 2

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Let the radius of inner circle be r

Given, Circumference of inner circle = 44 cm.

∴ C = 44 cm

⇒ C = 44

⇒ 2πr = 44

⇒ πr = 22

⇒r = 7 cm.

Now, Let the radius of outer circle be R

Given, Circumference of inner circle = 88 cm.

∴ C = 88 cm

⇒ C = 88

⇒ 2πR = 88

⇒ πR= 44

⇒ R= 14 cm.

Width of the path = R - r = 14 - 7 = 7cm.

Area of inner circle

⇒a = πr²

⇒a = π(7)²

⇒a = 49π

Area of Outer circle

⇒A = πR²

⇒A = π(14)²

⇒A = 196 π

Area of the Path

= A - a

= (196 - 49) π

= 147 π

= 147 ( 22) / 7

= 21 ( 22)

= 462 cm²

Therefore, Area of the path is 462 cm².

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