A copper solid cylinder of radius 14 cm and height 10cm is meter and recast into cylindrical wire of diameter 4mm.find the length of
copper wire?
Convert cm to mm by multiplying by 10.
V = πr^2h = π * 140^2 * 100 = π * 19600 * 100 = 1,960,000π
1,960,000π = π2^2h = π4h
Solve for h = length
To find the length of the copper wire, we need to determine the volume of the copper solid cylinder and then calculate the length of the cylindrical wire it is recast into.
Step 1: Calculate the volume of the copper solid cylinder
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. In this case, the radius (r) is given as 14 cm and the height (h) is given as 10 cm.
Therefore, the volume (V) of the copper solid cylinder can be calculated as:
V = π(14 cm)^2 * 10 cm = 6160 π cubic cm
Step 2: Calculate the volume of the cylindrical wire
Since the copper solid cylinder is recast into a cylindrical wire, the volume of the cylindrical wire will be the same as the volume of the copper solid cylinder.
Therefore, the volume of the cylindrical wire is also 6160 π cubic cm.
Step 3: Calculate the length of the cylindrical wire
We can use the volume of the cylindrical wire (6160 π cubic cm) and the formula for the volume of a cylinder (V = πr^2h) to solve for the length (h) of the cylindrical wire.
To find the diameter (D) of the cylindrical wire, we need to divide the given diameter by 2:
D = 4 mm ÷ 2 = 2 mm
Converting the diameter to radius: r = D/2 = 2 mm ÷ 2 = 1 mm = 0.1 cm (since 1 cm = 10 mm)
Now, we can rewrite the formula for the volume of a cylinder as:
6160 π = π(0.1 cm)^2 * h
h = (6160 π) / (π(0.1 cm)^2)
h = (6160 π) / (π(0.01 cm^2))
h ≈ 616000 cm
Therefore, the length of the copper wire is approximately 616,000 cm.