A cuboidal slab of copper having dimensions 22 cm × 10 cm × 5 cm is melted and recasted in the form of a wire of 1 mm diameter. The wire is rubber coated at the rate of Rs. 1.50 per meter. Find the cost of rubber coating (in ₹) \(\left(\text{Use } \pi=\displaystyle\frac{22}{7}\right)\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2100
Recasting keeps the volume of copper the same, so the wire is a long cylinder whose volume equals the slab’s. Its length then gives the cost of coating, charged per metre.
The wire’s length (volume of slab = volume of wire):
Volume of the slab \(=22\times10\times5=1100\,\mathrm{cm^3}\)
Radius of the wire \(=0.5\) mm \(=0.05\) cm
\(\displaystyle \frac{22}{7}\times0.05\times0.05\times h=1100\)
\(\displaystyle h=\frac{1100\times7}{22\times0.0025}=140000\) cm \(=1400\) m
The cost of coating (Rs. 1.50 per metre):
Cost \(=1400\times1.50=\) ₹2100
Tip: Change the diameter of 1 mm into centimetres (radius 0.05 cm) before using it with a volume in cm3, and the length from cm into metres before using the rate per metre.