A rectangular piece of iron sheet measuring 50 cm by 100 cm is rolled into a cylinder of height 50 cm. If the cost of painting the cylinder is Rs. 50 per square metre, then what will be the cost of painting the outer surface of the cylinder ?

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Q: 140 (IAS/2000)
A rectangular piece of iron sheet measuring 50 cm by 100 cm is rolled into a cylinder of height 50 cm. If the cost of painting the cylinder is Rs. 50 per square metre, then what will be the cost of painting the outer surface of the cylinder ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,1,1,0,1,0

keywords: 

{'iron sheet': [0, 1, 0, 0], 'rectangular piece': [0, 1, 0, 1], 'cylinder': [0, 2, 1, 2], 'outer surface': [0, 1, 0, 0], 'square metre': [0, 1, 0, 0], 'cost': [2, 1, 2, 10]}

The rectangular piece of iron sheet is rolled into a cylinder, which means the length of the rectangle becomes the circumference of the cylinder. The given length of the rectangle is 100 cm, which becomes the circumference of the cylinder.

Circumference of the cylinder = 100 cm

To find the radius of the cylinder, we can use the formula for the circumference of a circle:

Circumference = 2?r

100 = 2?r

r = 50 / ? cm

Now, let`s calculate the area of the outer surface of the cylinder:

Outer surface area = 2?rh

Since the height of the cylinder is also given as 50 cm, we can substitute the values:

Outer surface area = 2? * (50 / ?) * 50 = 5000 cm²

To convert the area to square meters, we divide by 10000:

Outer surface area = 5000 cm² / 10000 = 0.5 m²

Finally, we multiply the area by the cost per square meter:

Cost of painting the outer surface = 0.5 m² * Rs. 50/m² = Rs. 25.00

Therefore, the correct answer is Rs. 25.00, which aligns with option (a).

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