How many iron rods, each of length 7 meter, and diameter 2 cm can be made out of 0.88 cubic meter of iron?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 400
Each rod is a cylinder of volume \(\pi r^{2}h\). The number of rods is the volume of iron divided by the volume of one rod, with every length in metres first.
Radius: \(r=\frac{2}{2}=1\,\mathrm{cm}=0.01\,\mathrm{m}\); length \(h=7\,\mathrm{m}\)
Volume of one rod: \(\displaystyle\frac{22}{7}\times0.01^{2}\times7=22\times0.0001=0.0022\,\mathrm{m^3}\)
Number of rods: \(\displaystyle\frac{0.88}{0.0022}=\) 400
Tip: The diameter is in centimetres and the rest in metres; leaving 1 cm as 1 in the formula is the usual slip in such questions.