Question

Circular ground radius 35m.7m wide path is around the ground on its inside. Find the area of the path?

Answer 1

AnswEr :

⋆ Reference of Image is in the attachment :

• Radius₁ ( R ) = 35 m
• Radius₂ ( r ) = (35 - 7) = 28 m
• Find the Area of Path?

• According to the Question Now :

⇒ Area of Path = ( Area of Outer Circle – Area of Inner Circle )

⇒ Area of Path = πR² – πr²

⇒ Area of Path = π(R² – r²)

⇒ Area of Path = π{(35)² – (28)²}

• (a² - b²) = (a + b)(a - b)

⇒ Area of Path = π(35 + 28)(35 – 28)

⇒ Area of Path = π × 63 × 7

⇒ Area of Path = 22 /7 × 63 × 7

⇒ Area of Path = ( 22 × 63 ) m²

⇒ Area of Path = 1386 m²

∴ Hence, Area of Path will be 1386 m².

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• Shortcut Trick :

To find the Area of a Circle ; Check if Radius is Divisible by 3.5 in whole number or not,if Divisible then Use this Trick.

1.) First Divide Radius by 3.5

2.) Square the Outcome and Multiply it by 38.5 to get the Area of Circle.

⋆ Area of Circle = 38.5 × ( Radius /3.5 )²

• Here Area of Inner Circle :

⇒ 38.5 × ( 28 /3.5)²

⇒ 38.5 × ( 8 )²

⇒ 38.5 × 64

⇒ 2464 m²

• Here Area of Outer Circle :

⇒ 38.5 × ( 35 /3.5)²

⇒ 38.5 × ( 10 )²

⇒ 38.5 × 100

⇒ 3850 m²

• Area of the Circular Path will be :

⇒ Area of (Outer Circle – Inner Circle)

⇒ 3850 m² – 2464 m²

⇒ 1386 m²

∴ Hence, Area of Circular Path is 1386 m².

_________________________________

• Here is Quick Format to Remember :

⋆ Radius ⠀⠀⠀Circumference ⠀⠀⠀Area

⠀3.5 ⠀⠀⠀⠀⠀⠀⠀⠀⠀22 ⠀⠀⠀⠀⠀⠀⠀⠀38.5

⠀7 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀44 ⠀⠀⠀⠀⠀⠀⠀⠀154

⠀10.5 ⠀⠀⠀⠀⠀⠀⠀⠀66 ⠀⠀⠀⠀⠀⠀⠀⠀346.5

⠀14 ⠀⠀⠀⠀⠀⠀⠀⠀⠀ 88⠀⠀⠀⠀⠀⠀⠀⠀ 616

Answer 2

Answer:

$\large\bold\red{1386\:{m}^{2}}$

Step-by-step explanation:

Given,

A Circular ground having,

• Radius, R = 35 m

Also,

A path is all inside the ground such that,

• Width = 7 m

Clearly,

Radius of the inner circle will be,

• Radius, r = 35-7 = 28 m

$\pink{Note:-}$Refer to the attachment for diagram.

Now,

The area of the path will be,

$\large \boxed{ \bold \purple{Area,A = \pi( {R}^{2} - {r}^{2} )}}$

Putting the values,

We get,

$= > A = \pi( {(35)}^{2} - {(28)}^{2} ) \\ \\ = > A = \frac{22}{7} \times (35 + 28)(35 - 28) \\ \\ = > A = \frac{22}{7} \times 63 \times 7 \\ \\ = > A = 22 \times 63 \\ \\ = > A = 1386$

Hence,

Area of the path = $\bold{1386\:\:{m}^{2}}$