Question

A garden in shape of a circle has an area of 31,400m². Find the cost of fencing it at the rate ₹ 10/m.​

Answer 1

Solution :

We are given area if the circle and asked to find cos of fencing circle.

Fencing the circle mease enclosing with fence around any land.

Therefore we need to find the perimeter i.e Circumference of the circle.

To find cicumference we need to know the radius of the circle too.

So, let's start solving.

Area of the circle = 31400 cm²

Also, Area of the circle = πr²

[ Where r = Radius of the circle ]

⇒ πr² = 31400

⇒ 3.14 * r² = 31400

[ π is aprox equal to 3.14 ]

⇒ r² = 31400/3.14

⇒ r² = 3140000/314

⇒ r² = 10000

⇒ r = √10000

⇒ r = 100

Circumference of the circlr = 2πr

= 2 * 3.14 * 100

[ π is aprox equal to 3.14 ]

= 2 * 314

= 628 m

Cost of fencing 1 m = Rs.10

Cost if fencing the circle = 628 * 10 = Rs. 6280

Hence, cost of fencing the garden is Rs. 6280.

Answer 2

Given :-----

• Area of garden in shape of circle is = 31,400m²
• cost of fencing = Rs.10/m

Formula used :-----

• Area of circle = πr²
• Circumference of circle = 2πr
• π = 3.14

it is given that area of circle is = 31400m²

so,

πr² = 31400

→ 3.14 × (r²) = 31400

→ (r²) = (31400/3.14) = 10000

square root both sides,

→ r = √10000 = 100m

Now, fencing will be done outside the square ,

so, we have to find circumference of garden.

Circumference = 2πr

→ Circumference = 2×3.14 × 100

→ Circumference = 628m

Hence , cost of Fencing will be :-- 628 × 10 = Rs.6280

(Hope it Helps you)