Question

Question 1
A copper wire, 3 mm in diameter is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per $c{m}^3$.

Answer 1

For copper wire: Diameter = 3 mm = 0.3 cm (10mm= 1cm)
For cylinder; length h = 12 cm, d = 10 cm
Density of copper = 8.88 gm per $c{m}^3$
Curved surface area of cylinder can be calculated as follows:
$=2\pi rh$
=$\pi \times 10\times 12$
$=120\pi c{m}^2$
Length of wire can be calculated as follows:
$Length\left(h\right)=\frac{Area}{Width}$
$=\frac{120\pi }{0.3}=400\pi$
$=1256cm$
Now, volume of wire can be calculated as follows:
$V=\pi r^{2}h$
$=3.14\times {0.15}^2\times 1256$
$=88.7364c{m}^3$
Mass can be calculated as follows:
$Mass=Density\times Volume$
$=8.88\times 88.7364$
$=788g\left(approx\right)$