Questions

(i) A CIRCULAR pond of diameter 28 m is surrounded by a path 7 m wide. Find the area of the path.

(II) Find the area of a 2 m wide circular path surrounding a circular plot of radius 20 m.

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Answers

(i)

Given

• The diameter of circular pond is 28 m
• The pond is surrounded by a path 7 m wide

To Find

• The Area of the Path

Solution

Area of Path ⇒ Area of the Pond with Path - Area of the Pond

Radius of Pond ⇒ = 21 m

Radius of Pond along with Path ⇒ 27 - 7 = 14 m

Area of Path ⇒ π (R² - r²)

⇒ π {(21)² - (14)²}

⇒

⇒

⇒

⇒

⇒ 770 m²

∴ The area of the path is 770 m²

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(ii)

Given

• The radius of the circular plot is 20 m
• The circular plot is surrounded with a 2 m wide circular path.

To Find

• The Area of the Path

Solution

Area of Path ⇒ Area of the Plot with Path - Area of the Plot

Radius of Plot ⇒ 20 + 2 = 22 m

Radius of Plot along with Path ⇒ 22 - 2 = 20 m

Area of Path ⇒ π (R² - r²)

⇒ π {(22)² - (20)²}

⇒

⇒

⇒

⇒

⇒ 264 m²

∴ The area of the path is 264 m²

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