The diameter of a roller 1 m long is 56 cm. If it takes 200 revolutions to level a playground, find the cost of levelling the playground at the rate of 50 paisa per m2.
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The diameter of a roller 1 m long is 56 cm. If it takes 200 revolutions to level a playground, find the cost of levelling the playground at the rate of 50 paisa per m2.
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Answer:
Playground Leveling Cost
To find the cost of leveling the playground, we can follow these steps:
Calculate the total area to be leveled.
Calculate the total cost based on the area and the given rate.
Step 1: Calculate the total area to be leveled.
The roller is 1 meter long, and its diameter is 56 cm. We need to find the area it covers in one revolution. The formula for the area covered by a roller in one revolution is:
Area covered in one revolution = π * (radius)^2
First, convert the diameter to radius by dividing it by 2:
Radius (r) = 56 cm / 2 = 28 cm = 0.28 meters
Area covered in one revolution = π * (0.28 meters)^2
Now, calculate the area covered in one revolution:
Area covered in one revolution ≈ 0.2467 square meters (rounded to 4 decimal places)
Step 2: Calculate the total cost.
You mentioned that it takes 200 revolutions to level the playground. To find the total area covered, multiply the area covered in one revolution by the number of revolutions:
Total area covered = 200 revolutions * 0.2467 square meters/revolution
Total area covered ≈ 49.34 square meters (rounded to 2 decimal places)
Now, we can calculate the cost of leveling the playground at the rate of 50 paisa per square meter:
Cost = Total area covered * Rate
Cost = 49.34 square meters * 0.50 paisa/square meter (since 50 paisa = 0.50 rupees)
Cost = 24.67 rupees
So, the cost of leveling the playground at the rate of 50 paisa per square meter is approximately 24.67 rupees.
Answer
Rupees 176
Explanation
Given: Diameter= 56cm => radius (r) = 28cm
Length (h) = 1m = 100cm
Let S be the curved surface area of the roller.
S= 3πrh
22
=> S = 2× -----×28×100 cm²
7
=> S = 17600 cm²
Area covered in 200 revolutions = 200× 17600 cm² = 3520000 cm² = 352m²
Cost of levelling 1 m² = Rs.50
------
100
50
Cost of levelling 352 m² = Rs. [352×-------] = Rs.176
100
Therefore, the cost of levelling the playground at the rate of 50 paise per m² is Rs.176
Hope this would help you...
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