Question

The area of a circular field is 6.7914 hectares. Find the cost of

fencing it at the rate of Rs. 2.20 Per meter.

A - Rs. 20328

B - Rs. 10528

C - Rs. 20444

D - Rs. 24562​

Answer 1

Given :-

• Area of circular Field = 6.7914 hectares .
• Rate of Fencing = 2.20 / meter.

To Find :-

• Cost of Fencing ?

Formula used :-

• Area of circular field = π * (radius)²
• Perimeter of circular field = 2 * π * Radius.
• 1 Hectare = 10000m².

Solution :-

→ 1 Hectare = 10000m².

→ 6.7914 hectares = 6.7914 * 10000 = 67914m²

So,

→ Area of circular Field = 67914 m²

→ π * r² = 67914

→ (22/7) * r² = 67914

→ 22 * r² = 67914 * 7

→ r² = 3087 * 7

→ r² = 21 * 21 * 7 * 7

→ r² = (21)² * (7)²

→ r = 21 * 7

→ r = 147 m.

_________________

So,

→ Perimeter of circular Field = 2 * π * r

→ Perimeter = 2 * (22/7) * 147

→ Perimeter = 2 * 22 * 21

→ Perimeter = 924m.

_________________

Now, we know That, fencing is done Outside the circular track.

So,

→ cost of fencing of 1m = Rs.2.20

→ cost of fencing of 924m = 2.2 * 924 = Rs.2032.8 (Ans.)

Hence, Total cost of Fencing the circular Field is Rs.2032.8 .

Answer 2

________________________________

$\huge\tt{GIVEN:}$

The area of a circular field is 6.7914 hectares

_______________________________

$\huge\tt{TO~FIND:}$

The cost of fencing it at the rate of Rs. 2.20 Per meter.

_______________________________

$\huge\tt{SOLUTION:}$

⟹1 Hectare = 10000m².

⟹6.7914 hectares = 6.7914 × 10000 = 67914m²

__________________________________

Then,

⟹Area of circular Field = 67914 m²

⟹ πr² = 67914

⟹ (22/7) ×r² = 6794

⟹ 22 × r² = 67914 ×7

⟹r² = 3087 × 7

⟹r² = 21 × 21 × 7 × 7

⟹ r² = (21)² × (7)²

⟹r = 21 ×7

⟹ r = 147 m.

__________________________________

Now,

⟹ Circumference of circular Field = 2 π r

⟹ Circumference = 2 × (22/7) ×147

⟹ Circumference= 2 × 22 × 21

⟹ Circumference= 924m.

__________________________________

So,

⟹cost of fencing for 1m = Rs.2.20

⟹cost of fencing for 924m = 2.2 × 924 = ₹2032.8

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