Question

a cost of fencing at the rate of ​

Answer 1

Question:-

The cost of fencing a circular field at the rate of Rs. 24 per m 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:-

Let the radius of the field be r m.

Given:

Cost of fencing the field per m = Rs. 24

Total cost of fencing = Rs. 5280.

We know,

Perimeter = Total cost of fencing/Cost of fencing per m.

So,

⟶ Perimeter of the field = 5280/24

⟶ Perimeter of the field = 220 m

Now,

Perimeter/Circumference of a circle = 2πr

⟶ 2πr = 220

⟶ r = 220 × (1/2) × (7/22)

⟶ r = 35 m

And also given that,

Cost of ploughing the field = Rs. 0.50/m

We know,

Area of a circle = πr²

⟶ Area of the field = (22/7) * (35)²

⟶ Area of the field = 3850 m²

Now,

Total cost of ploughing = Cost of ploughing × Area of the field

So,

⟶ Total cost of ploughing = 0.50 × 3850

⟶ Total cost of ploughing = Rs. 1925

∴ It costs Rs. 1925 to plough the field.

Answer 2

Answer:

✯ Given :-

• The cost of fencing a circular field at the rate of Rs 24 per m is Rs 5280.
• The field is to be ploughing at the rate of Rs 0.50 per m².

✯ To Find :-

• Find the cost of ploughing of the field.

✯ Solution :-

⋆ Given :-

» Total, cost of fencing the circular field is Rs 5280

» Rate of fencing the circular field is Rs 24 per m

» Rate of ploughing the circular field is Rs 0.50 per m²

➽ We know that, Length of the circular field,

✪ $\dfrac{Total\: cost}{Rate}$ ✪

⇒$\sf\dfrac{\cancel{5280}}{\cancel{24}}$

⇒220 m

» Let, the radius be r

➙ Circumference = 220 m

➣ According to the question,

⇒2πr = 220

⇒r = $\dfrac{220}{2π}$

⇒r = $\dfrac{220 × 7}{2 × 22}$

⇒r = 35 m

↦ Radius of the field is 35 m

➼ Again, we know that, Area of the circular field = πr²

⇒$\dfrac{22}{7}$ × (35)²

⇒$\dfrac{22}{7}$ × 35 × 35

⇒ 22 × 5 × 35 m²

➠ 3850 m²

Hence, the cost of ploughing the field,

⇒3850 × 0.50

➨ Rs 1925

$\therefore$ The cost of ploughing the field is $\boxed{\bold{\large{\rm{\red{Rs\: 1925}}}}}$

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