Question

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 ${cm}^3$.

Answer 1

Cylinder
Diameter = 10 cm
radius $=r=\frac{d}{2}=\frac{10}{2}=5$ cm
Length of wire one round of cylinder = circumference of base 2 $\pi$ r = 2 $\pi$ r = 10 $\pi$ cm
Cylindrical wire diameter = 3mm
= $\frac{3}{10}$ cm
length of cylinder = h = 12 cm
Total round $=\frac{heightofcylinder}{0.3}$
$=\frac{12}{0.3}=40$
Total round = 40
Now, length of wire required in one round = circumference of base of cylinder
$2\pi r=2\pi \times \frac{10}{2}$
$2\pi r=10\pi$ cm
Hence in 40 round the length of wire required
$=40\times 10\pi$
$=400\pi$ cm
$=\frac{400\times 22}{7}=1257.14$ cm
$=12.57$ m
therefore total length of wire 12.57 m
volume of wire $=\pi r^{2}h$
$=\pi \times (\frac{0.3}{2}{)}^2\times 1257.14$
= 88.898 cm${}^3$
The mass of wire of 1 cm${}^3$ = 8.885
$\therefore$ the mass of wire of 88.898 cm${}^3$
= 8.88 x 88.898
= 798.413
Hence mass of wire = 798.419 and length of wire = 12,57 m