A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Question
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Solution
To find the thickness of the wire, we can use the formula for the volume of a cylinder.
First, let's find the volume of the copper rod. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the diameter of the copper rod is 1 cm, we can find the radius by dividing the diameter by 2. So, the radius (r) of the copper rod is 1 cm / 2 = 0.5 cm = 0.005 m.
The height (h) of the copper rod is given as 8 cm = 0.08 m.
Now, we can calculate the volume of the copper rod using the formula:
V_rod = π(0.005)^2(0.08)
Next, let's find the volume of the wire. We know that the length of the wire is 18 m.
The volume of the wire can be calculated using the formula:
V_wire = πr^2h
We need to find the radius (r) and height (h) of the wire.
Since the wire has uniform thickness, the radius of the wire will be the same as the radius of the copper rod, which is 0.005 m.
The height of the wire (h_wire) can be calculated using the formula:
h_wire = V_wire / (πr^2)
We know that the volume of the wire (V_wire) is equal to the volume of the copper rod (V_rod).
So, we can substitute the values and solve for h_wire:
h_wire = V_rod / (π(0.005)^2)
Finally, we can find the thickness of the wire by subtracting the height of the copper rod from the height of the wire:
thickness = h_wire - h
Substituting the values, we can calculate the thickness of the wire.
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