Question

The cost of fencing a circular field at rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m². Find the cost of ploughing the field.​

Answer 1

✬ Cost = Rs 1925 ✬

Step-by-step explanation:

Given:

• Cost of fencing circular field at rate of Rs 24 /m is 5280.
• Rate of ploughing per m² is Rs 0.50.

To Find:

• Total cost of ploughing the field.

Solution: Here in first , we have to find the circumference of the field.

➟ Circumference = Total cost/cost per metre.

➟ 5280/24

➟ 220 cm

Let the radius of field be r cm.

As we know that

★ Circumference = 2πr ★

★ Area of Circle = πr² ★

$\implies{\rm }$ 220 = 2πr

$\implies{\rm }$ 220 = 2 × 22/7 × r

$\implies{\rm }$ 220 × 7/44 = r

$\implies{\rm }$ 5 × 7 = r

$\implies{\rm }$ 35 = r

• Radius of circular field is 35 m.

$\implies{\rm }$ Area = 22/7 × 35²

$\implies{\rm }$ 22 × 5 × 35

$\implies{\rm }$ 3850 m²

➮ Cost of ploughing per m² = Rs 0.50

➮ Cost of ploughing 3850 m² = 3850 × 0.50 = Rs 1925.

Answer 2

Given :

• Cost of fencing a circular field at the rate of Rs. 24 per metre is Rs. 5280.

• The field is to be ploughed at the rate of Rs 0.50 per m².

To Find :

• Find the cost of ploughing the field.

Solution :

$\sf : \implies \: \: \: \: \: \: Circumference \: of \: circle =</p><p> \cancel{\frac{5280}{24} }\\ \\ \\ \sf : \implies \: \: \: \: \: \: Circumference \: of \: circle = 220 \:$

we know :

$\sf : \implies \: \: \: \: \: \: \: 2 \times \frac{22}{7} \times r = 220 \: \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:44r \: = 1540 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: r = \cancel{\frac{1540}{44} } \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: r = 35$

$\\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: Area \: of \: circle = </p><p>\pi {r}^{2}</p><p>$

Substitute all values :

$\sf : \implies \: \: \: \: \: \: \: \: \: = \frac{22}{ \cancel{7}} \times \cancel{35 }\times 35 \: \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: = 22 \times 5 \times 35 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: = 3850 \: {m}^{2}$

According to the Question :

$\sf : \implies \: \: \: \: \: \: \: \: 3850 = 3850 \times 0.50 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 192.50$