#### Question

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

#### Solution

Given diameter of copper rod(d_{1}) = 1cm

Radius`(r_1)=1/2=0.5cm`

Length of copper rod (h_{1}) = 8cm

Volume of cylinder`=pir_1^2h_1`

`V_1=pi(0.5)^2xx8cm^3` ........(1)

`V_2=pir_2^2h_2`

Length of wire(h_{2}) = 18m = 1800cm

`V_2=pir_2^2(1800)cm^3` ........(2)

Equating (1) and (2)

V_{1} = V_{2}

`pi(0.5)^2xx8=pir_2^2(1800)`

`(pi(0.5)^2xx8)/(pi(1800))=r_2^2`

r_{2} = 0.033cm

∴Radius thickness of wire = 0.033cm .

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Solution A Copper Rod of Diameter 1cm and Length 8cm is Drawn into a Wire of Length 18m of Uniform Thickness. Find Thickness of Wire? Concept: Volume of a Combination of Solids.