A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find the thickness of the wire.

Finding the Thickness of the Wire

To determine the thickness of the wire drawn from a copper rod, we can utilize the principle of volume conservation. The volume of the copper rod must equal the volume of the wire.

• Step 1: Calculate the volume of the copper rod

The formula for the volume of a cylinder is given by:

    V = ext{Area} imes ext{Height}

Where the area of the base is:

    A = rac{ ext{π}d^2}{4}

For the copper rod:

• Diameter ( ext{d}) = 1 ext{ cm} = 0.01 ext{ m}
• Length ( ext{h}) = 8 ext{ cm} = 0.08 ext{ m}

Substituting the values:

    V_{rod} = rac{ ext{π}(0.01)^2}{4} imes 0.08

     ext{Calculating: }     V_{rod} ext{ (approx.) } = 6.2832 imes 10^{-5} ext{ m}^3

• Step 2: Calculate the volume of the wire

Let the thickness of the wire be ext{t} (in meters). The volume of the wire can be represented as:

    V_{wire} = rac{ ext{π}t^2}{4} imes ext{Length}

Where the length of the wire = 18 ext{ m}:

    V_{wire} = rac{ ext{π}t^2}{4} imes 18

• Step 3: Equate the volumes

Setting the volumes equal:

    V_{rod} = V_{wire}

    6.2832 imes 10^{-5} = rac{ ext{π}t^2}{4} imes 18

• Step 4: Solve for ext{t}

Rearranging gives:

    t^2 = rac{6.2832 imes 10^{-5} imes 4}{ ext{π} imes 18}

Calculating this yields:

    t ext{ (approx.) } = 0.0025 ext{ m} = 2.5 ext{ mm}

Conclusion: The thickness of the wire is approximately 2.5 mm.

Memory Tip: Remember that the volume remains constant during the drawing process, making it essential to equate the volumes of both shapes.