Question

A copper wire of 4 mm diameter is evenly wound about a cylinder whose length is 24 cm and diameter 20 cm so as to cover whole surface. Find the length

Answer 1

Answer:

The length of wire would be 600 cm

Step-by-step explanation:

A copper wire of 4 mm diameter is evenly wound about a cylinder whose length is 24 cm and diameter 20 cm so as to cover whole surface.

A copper will also like a thin cylinder whose diameter is 4 mm.

Let length of wire be h cm

Radius of wire = 4/2 = 2 mm = 0.2 cm

Surface area of wire = $2\pi rh$

Surface of wire = $0.4\pi h$

For cylinder, Radius (r)= 10 cm and Height (h)= 24 cm

Surface area of Cylinder =$2\pi rh$

Surface area of Cylinder =$2\pi 10\times 24=480\pi$

Surface area cylinder = 2 times surface area of wire

$480\pi=2 \times 0.4\pi h$

$h=\dfrac{480\pi}{0.8\pi}$

$h=600\text{ cm}$

Thus, The length of wire would be 600 cm

Answer 2

Answer:

Length of the cylinder = 24 cm Diameter of copper wire = 4 mm = 0.4 cm

Therefore, the number of rounds of wire to cover the length of cylinder

Now, diameter of cylinder = 20 cm

Therefore, length of wire in one round = circumference of base of the cylinder = d cm

Length of wire for covering the whole surface of cylinder = length of wire in 60 rounds

Radius of copper wire = cm = 0.2 cm

Therefore, volume of wire = r2h

= 474.122 cu. cm

Weight of wire = volume × density = 474.122 × 8.68 gm = 4115.38 gm = 4.11538 kg 4.12 kg

Step-by-step explanation: