A factory makes 1,20,000 pencils daily. Each pencil is a cylinder of length 25 cm and base circumference 1.5 cm. Find the cost of colouring the curved surfaces at Rs 0.05 per dm².
Rs 2,250
Step 1: Recall formula
The curved surface area (CSA) of a cylinder is:
\( CSA = \text{circumference of base} \times \text{height} \).
Step 2: Write given values
Height (length of pencil) = \( 25\,\text{cm} \).
Circumference of base = \( 1.5\,\text{cm} \).
Step 3: Find CSA of 1 pencil
\( CSA = 1.5 \times 25 = 37.5\,\text{cm}^2 \).
Step 4: Total CSA for all pencils
Number of pencils = \( 1,20,000 = 1.2 \times 10^5 \).
Total CSA = \( 37.5 \times 1.2 \times 10^5 = 4.5 \times 10^6\,\text{cm}^2 \).
Step 5: Convert into dm² (SI requirement)
Recall: \( 1\,\text{dm} = 10\,\text{cm} \Rightarrow 1\,\text{dm}^2 = 100\,\text{cm}^2 \).
So, \( 4.5 \times 10^6\,\text{cm}^2 = \dfrac{4.5 \times 10^6}{100} = 45{,}000\,\text{dm}^2 \).
Step 6: Find cost of colouring
Cost per dm² = Rs 0.05.
Total cost = \( 45{,}000 \times 0.05 = 2{,}250 \).
Final Answer: Rs 2,250