Question

A silver rod of radius 0.5 cm and length 16 cm is drawn into a wire of uniform thickness of length 36 m. What will be the thickness of the wire?​

Answer 1

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Answer 2

Thickness of the wire will be about 0.0667 cm if A silver rod of radius 0.5 cm and length 16 cm is drawn into a wire of uniform thickness of length 36 m.

Given:

• A silver rod of radius 0.5 cm and length 16 cm
• Drawn into a wire of uniform thickness of length 36 m

To Find:

• Thickness of the wire

Solution:

• Volume of cylinder = πr²h
• r = radius of cylinder
• h = height of cylinder
• 1 m = 100 cm
• Diameter = 2 x Radius

Step 1:

Calculate volume of silver rod by substituting r = 0.5 cm , h = 16 cm

V= π(0.5)²16

V = π (0.25)16

V = 4π  cm³

Step 2:

Calculate volume of wire by substituting h = 36 m = 3600 cm and equate with Volume of silver rod and solve for r

π(r)²(3600) = 4π

r² = 1/900       ( Dividing both sides by 3600π)

r = 1/30           ( taking square root both sides and considering only +ve Value)

Step 3:

Diameter of wire = Thickness of wire hence multiply radius with2 to find thickness

Thickness = 2 x radius

Thickness = 2 x 1/30  cm

Thickness = 1/15  cm

Thickness ≈ 0.0667 cm

Thickness of the wire will be about 0.0667 cm