Question

A factory manufactures $120000$ 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 $\mathrm{Rs}0.05\mathrm{per}{\mathrm{dm}}^2.$

Answer 1

Step 1: Writing the given information

The shape of pencil is cylindrical.

Number of pencils manufactured in a day$=120000$

Circumference of base of cylinder$=1.5\mathrm{cm}$

Height of cylinder$=25\mathrm{cm}$

Cost for colouring $1{\mathrm{dm}}^2=₹0.05$

Step 2: Finding out the radius

Circumference of circle is $2\mathrm{\pi r}=1.5\mathrm{cm}$

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

Step 3: Finding out the curved surface area of cylinder

Curved surface area of cylinder$=2\mathrm{\pi rh}$

Curved surface area of pencil$=2\mathrm{\pi }\left(\frac{1.5}{2\mathrm{\pi }}\right)25=37.5{\mathrm{cm}}^2$

$$\begin{gathered} 1\mathrm{cm}=0.1\mathrm{dm} \\ \Rightarrow 1{\mathrm{cm}}^2=0.01{\mathrm{dm}}^2 \\ \Rightarrow 37.5{\mathrm{cm}}^2=0.375{\mathrm{dm}}^2 \end{gathered}$$

Step 4: To determine the cost of colouring the curved surfaces of the pencils manufactured in one day

Cost for colouring $1{\mathrm{dm}}^2=₹0.05$

Cost for colouring $0.375{\mathrm{dm}}^2(\mathrm{i}.\mathrm{e}.1\mathrm{pencil})=0.05\times 0.375=₹0.01875$

Cost for colouring $120000$ pencils$=120000\times 0.01875=₹2250$

Hence, cost for colouring $120000$ pencils$=₹2250$.