# A factory manufactures 1,20,000 pencils daily. The pencils are cylindrical inshape., each of length 25cm and circumference 1.5cm. Determine the cost of colouring the curved surface of the penciles manufactured in one day at Rs0.05 per dmÂ².

One pencil -:

$h = 25cm, and 2\pi r = 1.5 \\ then , r = \frac{1.5}{2\pi} \\$

Curved surface area for one pencil

$= 2\pi r h \\ = 2 \pi (\frac{1.5}{2\pi}) \times 25 \\ = 1.5 \times 25 \\ = 37.5 cm^{2} \\$

a given rate of coloring

$= Rs. 0.05/dm^{2} = \frac{0.05}{100}/ cm^{2}\\$

Cost of coloring   $120000 \\$ pencils

$120000 \times Rs. \frac{0.05}{100} \times37.5\\ = Rs. 2250 \\$

Hence, the Cost of coloring the curved surface of the pencils  $= Rs. 2250 \\$

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