1. A copper wire, 3 mm in diameter, iş 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?
Answers
Answer:
1256
Step-by-step explanation:
HOPE I HELP YOU TO FIND THE ANSWER
The length of the wire = 1256 cm
Mass of the wire = 788 gram
Step-by-step explanation:
Given:
A copper wire 3 mm in diameter is wounded about a cylinder 12 cm long
Diameter of cylinder = 10 cm
Density of copper = 8.88 g/cc
To find out:
Length and mass of the wire
Solution:
Length of cylinder H = 12 cm
Radius of the cylinder R = 10/2 = 5 cm
Radius of the wire r = 3 mm = 0.3 cm
Diameter of copper wire = 3 mm = 0.3 cm
One round of copper wire covers 0.3 cm of the cylinder
Therefore,
0.3 cm of the cylinder is covered in = 1 round
1 cm of the cylinder is covered in = 1/0.3 round
12 cm of the cylinder is covered in = 120/0.3 round = 40 round
Length of the wire required to complete one round will be equal to the circumference of the cylinder
Thus,
length of the wire = 2πR = 2 × 3.14 × (10/2) = 31.4 cm
Thus, length of the wire required to complete 40 round = 31.4 × 40 = 1256 cm
l = 1256 cm
Volume of the wire = πr²l = 3.14 × (0.3/2)² × 1256 cm³
Mass of the wire = Volume of the wire × Density
= (3.14 × 0.3² × 1256 × 8.88)/4
= 787.97 gram
≈ 788 gram
Hope this answer is helpful.
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