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A cylindrical pillar is 28 cm in diameter and 25 m in height. Find the cost of painting the curved surface of the pillar at the rate of ₹50 per m2. (Use π=722)
₹1100
₹1138
₹1080
₹1072
₹1100
Since the rate is ₹50, calculate area in m² and multiply by 50. Since 50 is half of 100, calculate the product and divide by 2 for quick mental math.
Diameter of pillar = 28 cm, Height = 25 m, Rate of painting = ₹50/m².
CSA=2×π×r×h
Since the rate is ₹50, calculate area in m² and multiply by 50. Since 50 is half of 100, calculate the product and divide by 2 for quick mental math.
Students often forget to convert the diameter from cm to meters, leading to a calculation error of 100 times the actual value.
Convert Units to Meters
Since the rate is per square meter and the height is in meters, convert diameter from cm to meters: d=28 cm=0.28 m.
d=0.28 m
Calculate Radius
The radius is half of the diameter.
r=20.28=0.14 m
Calculate Curved Surface Area
Use the formula for the curved surface area of a cylinder.
CSA=2×722×0.14×25=22 m2
Calculate Total Cost
Multiply the area by the rate of painting.
Total Cost=22×50=1100
A is correct because the calculated curved surface area is 22 m² and multiplying by the rate of ₹50 gives a total cost of ₹1100.
Always check units before starting calculation; in competitive exams, dimensions are often provided in mixed units (cm and m) to test unit consistency.
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