A copper solid cylinder of radius 14cm and height 10cm is melted and recast into cylindrical wire of diameter 4mm.find the length of the copper wire
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Give.the.answer
To find the length of the copper wire, we need to first calculate the volume of the copper cylinder and then use that to calculate the length of the wire.
First, let's calculate the volume of the copper cylinder:
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 radius of the copper cylinder is 14 cm and the height is 10 cm, we can use these values to calculate the volume.
V = π * (14 cm)^2 * 10 cm
V = π * 196 cm^2 * 10 cm
V = 1960π cm^3
Now let's calculate the length of the wire formed when the copper is recast into a cylindrical shape with a diameter of 4 mm.
The formula for the length of a wire is L = V / A, where L is the length, V is the volume, and A is the cross-sectional area of the wire.
The cross-sectional area of a cylindrical wire can be calculated using the formula A = πr^2, where A is the area and r is the radius.
Given that the diameter of the wire is 4 mm, the radius can be calculated as half of that:
r = 4 mm / 2 = 2 mm
Now let's convert the radius from millimeters to centimeters:
2 mm = 0.2 cm
Using this radius, we can calculate the cross-sectional area:
A = π * (0.2 cm)^2
A = π * 0.04 cm^2
Finally, we can use the volume of the copper cylinder and the cross-sectional area of the wire to calculate the length of the wire:
L = (1960π cm^3) / (π * 0.04 cm^2)
L = 1960 cm^3 / 0.04 cm^2
L = 49,000 cm
Therefore, the length of the copper wire formed when the copper cylinder is melted and recast into a cylindrical wire with a diameter of 4 mm is 49,000 cm.
I don't understand this solution
Maths
tumko kuchh nahi aata hai
volume cylinder= volume wire
PI(.14^2).10 m^3=PI(.004^2)L
solve for L.