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Question
A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per dm2.
Solution
The shape of pencil = cylinder.
Let the radius of base = r cm
Circumference of base = 1.5 cm
Circumference of circle is 2πr = 1.5 cm
r = `1.5/(2π) "cm"`
According to the question,
Height, h = 25 cm
We know that,
Curved surface area of cylinder = 2πrh
Curved surface area of pencil = `2π(1.5/(2π))25` = 37.5 cm2
1 cm = 0.1 dm
1 cm2 = 0.01 dm2
37.5 cm2 = 0.375 dm2
Cost for coloring 1 dm2 = Rs. 0.05
Cost for coloring 0.375 dm2 (i.e. 1 pencil) = Rs. 0.01875
Cost for coloring 120000 pencils = 120000 × 0.01875 = Rs. 2250
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