A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Answers
Answer:
1/30 cm (or) 0.033 cm
Step-by-step explanation:
(i)
Given, diameter of copper rod(d₁) = 1 cm.
Then, Radius (r₁) = 0.5 cm.
Given, length of copper rod(h₁) = 8 cm.
Volume of copper rod = πr₁²h₁
= π * (0.5)² * 8
= 2 π.
(ii)
Length of wire(h₂) = 18 m = 1800 cm.
Volume of wire = πr₂h₂
= πr₂(1800)
∴ Volume of copper rod = volume of wire.
⇒ 2 π = π * r₂² * 1800
⇒ r₂² = 1/900
⇒ r₂ = 1/30 (or) 0.033 cm
Therefore,Thickness of the wire = 0.033 cm.
Hope it helps!
Volume of the copper rod
Given :
diameter of rod = 1 cm
radius of the rod = 1 cm / 2
= 0.5 cm
height of the rod = 8 cm
Volume of a cylinder = π r² h
==> π ×( 0.5 cm )² × 8 cm
==> π × 0.25 cm² × 8 cm
==> π × 2 cm³
==> 2 π cm³ ..........................(1)
We know that : volume is always conserved whenever there is a change in shape .
Volume after the changed shaped
Let the thickness be r
height of the rod = 18 m
==> 18 × 100 cm
==> 1800 cm
Volume of a cylinder = π r² h
==> π ( r )² × 1800 cm ....................(2)
Thickness of the rod
Equation ( 1 ) = ( 2 )
2 π cm³ = π r² × 1800 cm
==> Cancelling 2 π cm both sides :
==> 1 cm² = 900 r²
==> r² = 1 / 900 cm ²
==> r = 1/30 cm [ Neglecting the negative value ]
==> r = 0.033 cm
The thickness of the rod is 0.033 cm
Hope it helps ya :)
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