Question

The cost of paving a circular room at rupees 12 per square metre is rupees 1848.Find the cost of fencing it at rupees 5 per metre. ​

Answer 1

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Length of the fence (in metres) = Total cost / Rate = 5280/24 = 220

So, circumference of the field = 220 m

Therefore, if r metres is the radius of the field, then

2πr = 220

or, 2 × 22/7× r = 220

or, r = (220 × 7)/(2 × 22) = 35

i.e., radius of the field is 35 m.

Therefore, area of the field = πr2 = 22/7 × 35 × 35 m2 = 22 × 5 × 35 m2

Now, cost of ploughing 1 m2 of the field = Rs 0.50

So, total cost of ploughing the field = Rs 22 × 5 × 35 × 0.50 = Rs 1925

Answer 2

Answer:

The cost of fencing the room is ₹220

Step-by-step explanation:

Given that,

• The cost of paving a circular shaped room is ₹1, 848 at the rate of 12/m².

To find :

• The cost of fencing the room at the rate of ₹5/m.

Step 1 :

➪ The area of the room is given by :

→ Total cost of paving/Rate of paving the floor.

→ 1848/12

→ 154m²

Therefore, the area of the floor is 154m² ✔

Step 2 :

✦ Finding the radius of the circular room :

➪ Area of the circle is given by : πr²

We have,

→ π = 22/7

→ Area = 154m²

→ Area of the circular-room : 22/7 • r²

→ 154 = 22/7 • r²

→ 154*7/22 = r²

→ 7*7 = r²

→ r = √7*7

→ r = √49

→ r = 7m

Step 3 :

✦ Finding the circumstance of the room :

• As we need to find the cost of fencing around the room we require the circumstance of the room.

→ Circumstance of a circular-room is given by :

→ 2πr

We have,

→ π = 22/7

→ r = 7m

→ Circumstance of the room : 2πr

→ 2 • 22/7 • 7

→ 2 • 22

→ 44metres.

So, the circumstance of the room is 44m ✔

Step 4 :

Finding the total cost of fencing :

Rate of fencing the room is ₹5 per m

∵ 1m² fencing costs ₹5

∴ 44metres of fencing will cost 5 • 44

→ ₹220 ✔