A copper solid cyliender of radius 14 cm and height 10 cm is melted and recast into cylienderI called wire of diameter 4mm find the length of the copper wire
That's cylindrical, not cylienderI called
Anyway, if the wire is of length x cm, then you need the volumes to be equal:
14^2 * 10 = 0.4^2 * x
now just find x.
close, but ... 14 cm is the RADIUS of the cylinder,
... while 4 mm is the DIAMETER of the wire
14^2 * 10 = (0.4 / 2)^2 * x
Dang! Way to watch!
man, this is not my day!
I gotta go...
To find the length of the copper wire, we need to calculate the volume of both the solid cylinder and the wire.
First, let's calculate the volume of the solid copper cylinder:
Volume of a cylinder = π * (radius)^2 * height
Given:
Radius of the copper cylinder = 14 cm
Height of the copper cylinder = 10 cm
Volume of the copper cylinder = π * (14 cm)^2 * 10 cm
Next, let's calculate the volume of the wire cylinder:
Volume of a cylinder = π * (radius)^2 * length
Given:
Radius of the wire cylinder = 4 mm = 0.4 cm
Since the diameter of the wire is given, we divide it by 2 to get the radius.
Now, we need to find the length of the wire. Let's assume the length is L cm.
Volume of the wire cylinder = π * (0.4 cm)^2 * L cm
According to the law of conservation of volume, the volume of the solid copper cylinder should be equal to the volume of the wire cylinder after melting and recasting.
So, we can equate the two volumes and solve for L (length of the wire):
π * (14 cm)^2 * 10 cm = π * (0.4 cm)^2 * L cm
Canceling out the π factor on both sides:
(14 cm)^2 * 10 cm = (0.4 cm)^2 * L cm
Simplifying:
1960 cm^3 = 0.16 cm^2 * L cm
Dividing both sides by 0.16 cm^2:
L cm = 1960 cm^3 / 0.16 cm^2
Now, we can calculate the length of the copper wire by dividing the volume of the solid copper cylinder by the cross-sectional area of the wire:
L cm = 12250 cm
Therefore, the length of the copper wire is 12250 cm.