Question

A steel 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 mass of the wire, assuming the density of steel to be 8.88 g per cm3

• A. 1038.48 gm
• B. 670.26 gm
• C. 734.12 gm
• D. 787.98 gm

Answer 1

The correct option is D

787.98 gm

Width of the wire used in one round =3 mm =0.3 cm
Number of rounds required to cover 12 cm of length =$\frac{12}{0.3}=40$
Diameter of the cylinder =10 cm
Radius of the cylinder =5 cm
Length of wire required for one round $=2\pi r=2\pi \times 5cm=10\pi cm$
Length of wire required for 40 round =$10\pi cm\times 40=400\times 3.14$
1256 cm.
Radius of wire =$\frac{3}{20}cm$
Volume of the wire =$\pi r^{2}h$
Weight of the wire =Volume of the wire $\times 8.88gm$
$3.14\times {\left(\frac{3}{20}\right)}^2\times 1256\times 8.88=787.98gm$