A factory manufactures 120,000 pencils daily The pencils are cylindrical in shape each of length $ 25 \mathrm{~cm} $ and circumference of base as $ 1.5 \mathrm{~cm} $. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $ ₹ 0.05 $ per $ \mathrm{dm}^{2} $.

Given:

A factory manufactures 120,000 pencils daily.

The pencils are cylindrical in shape each of length \( 25 \mathrm{~cm} \) and circumference of base as \( 1.5 \mathrm{~cm} \).

To do:

We have to find the cost of colouring the curved surfaces of the pencils manufactured in one day at \( ₹ 0.05 \) per \( \mathrm{dm}^{2} \).

Solution:

Length of each pencil $h= 25\ cm$

Circumference of the base of each pencil $= 1.5\ cm$

Let the radius of the base of the pencil be $r$.

This implies,

$2\pi r=1.5$

$\Rightarrow r=\frac{1.5}{2\pi}$

$\Rightarrow r=\frac{1.5 \times 7}{22 \times 2}$

$\Rightarrow r=0.2386 \mathrm{~cm}$

Curved surface area of each pencil $=2 \pi r h$

$=2 \times \frac{22}{7} \times 0.2386 \times 25$

$=\frac{262.46}{7}$

$=37.49 \mathrm{~cm}^{2}$

$=\frac{37.5}{100} \mathrm{dm}^{2}$        [Since $1 \mathrm{~cm}=\frac{1}{10} \mathrm{dm}$]

$=0.375 \mathrm{dm}^{2}$

This implies,

Curved surface area of 120000 pencils $=0.375 \times 120000$

$=45000 \mathrm{dm}^{2}$

Cost of colouring $1\ dm^2$ curved surface of the pencils manufactured in one day $= Rs.\ 0.05$

Therefore,

Cost of colouring $45000\ dm^2$ curved surface of the pencils $=Rs.\ 45000\times0.05$

$=Rs.\ 2250$

The cost of colouring the curved surfaces of the pencils manufactured in one day at \( ₹ 0.05 \) per \( \mathrm{dm}^{2} \) is Rs. 2250.

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Updated on: 10-Oct-2022

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