Question

A circular pond of radius 14m is surrounded by a path 7m wide. Find the

area of path
​

Answer 1

Correct Question:

A circular pond of Diameter 14m is surrounded by a path 7m wide. Find the area of path

Answer :

• Area of path is 462m²

Given :

• A circular pond of diameter is 14m is surrounded by a path is 7m wide

To find :

• Area of path

Solution :

As we know that

• Area of path = π(R² - r²)

Then,

⟶ R = 14/2 + 7 = 7 + 7 = 14 m

⟶ r = 14 - 7 = 7m

• Area of path = π(R² + r²)

⟶ π(14² - 7²)

⟶ π(196 - 49)

⟶ π(147)

⟶ 22/7 × 147

⟶ 462

⟶ 462m²

Hence , Area of path is 462m²

Answer 2

Given :-

• Radius of the Circular Pond is 14 m
• It is Surrounded by a path 7 m wide

To Find :-

• Area of that surrounded path

Solution :-

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

${\mid {\fbox{Area\;of\;path = \pi (R^{2} + r^{2} }}\mid}$${\mid {\boxed{Area\;of\;path = \pi ( R^{2} - r^{2} ) }}\mid}$

❒ Where ,

➺ R² = Radius of Pond + Width of Path

    = 14 + 7

    = 21 m  

➺  r² = Radius of Pond - Width of path

    = 14 - 7

    = 7 m

→ Now , let's solve by putting the values in this formula

$\sf \leadsto \dfrac{22}{7} \times ( 21^{2} - 7^{2} )$

$\sf \leadsto \dfrac{22}{7} \times ( 441 - 49 )$

$\sf \leadsto \dfrac{22}{7} \times 392$

$\sf \leadsto 22 \times 56$

$\sf \leadsto 1232 \; m^{2}$

∴ Area of the path is 1232 m²