**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 ₹ 0.05 per dm2.

**Solution:**

Given, pencils are cylindrical in shape.

Length of one pencil = 25 cm

and circumference of base = 1.5 cm

$\Rightarrow$ $r=\frac{1.5 \times 7}{22 \times 2}=0.2386 \mathrm{~cm}$

Now curved surface area of one pencil $=2 \pi r h$

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

$=\frac{262.46}{7}=37.49 \mathrm{~cm}^{2}$

$=\frac{37.49}{100} \mathrm{dm}^{2}$ $\left[\because 1 \mathrm{~cm}=\frac{1}{10} \mathrm{dm}\right]$

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

$\therefore$ Curved surface area of 120000 pencils $=0.375 \times 120000=45000 \mathrm{dm}^{2}$

Now. cost of colouring $1 \mathrm{dm}^{2}$ curved surface of the pencils manufactured in one day

$=₹ 0.05$

Cost of colouring 45000 dm2 curved surface = ₹ 2250