Question

The cost of fencing around a circular field at rupees 5 per metre is rupees 220 what is the total cost of cultivating the field at rupees 10 per square metre?
answer is : 1540
need explanation..​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Information Used:

• Area of circle = $\pi. {r}^{2}$
• Circumference = $2.\pi.r$ ----- ( 1 )

Given:

• Cost of fencing around a circular field at Rupees ₹ 5 Per metre is 220

To Find:

• The total cost of cultivating the field.
• At rate ₹ 10 per square metre.

Solution:

Cost of fencing the circumference = ₹ 220

Hence the circumference of circle = 220/5

Circumference = 44 m ------ ( 2 )

Using equation ( 1 ) in equation ( 2 )

$2.\pi.r= 44 m$

$2. (\frac{22}{7}) .r = 44m$

$r = 7$

Hence we obtain that Radius = 7 m

Cultivable land in the circle field = Area

Area of circle = $\pi. {r}^{2}$

Area = $(\frac{22}{7} ). {7}^{2}$

Area = 154 ${m}^{2}$

Cost of cultivating 1 m^2 field = ₹ 10

Hence cost of cultivating whole field = 154 x 10

Cost of cultivation = ₹ 1540

Cost of cultivating the field is ₹ 1540

Hence answer is ₹ 1540

Answer 2

Answer- The above question is from the chapter 'Areas Related to Circles'.

Concepts used: 1) Circumference of circle = Total cost of fencing ÷ Cost per metre

2) Area of circle = πr²

3) Cost of cultivating field = Area of circle × Cost per m²

Given question: The cost of fencing around a circular field at ₹ 5 per m is ₹ 220. What is the total cost of cultivating the field at ₹ 10 per m² ?

Solution: Circumference of circle = Total cost of fencing ÷ Cost per metre

2πr = ₹220 ÷ ₹5

2πr = 44

$\frac{22}{7}$ × r = 22

r = 7 m

Area of circular field = πr² = $\frac{22}{7}$ × 7 × 7 = 154 m²

Cost of cultivating per m² = ₹10

Cost of cultivating 154 m² = 154 × 10 = ₹1540

∴ Cost of cultivating the field = ₹1540.