Example 10

Transcript

Example 10 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. Volume of copper rod = Volume of wire Volume of copper rod Copper rod is in form of cylinder with Diameter of rod = 1 cm So, radius = r = 1/2 cm And, length = height = h = 8 cm Volume of copper rod = 𝜋𝑟2ℎ = π×(1/2)^2×8 = π× 1/4 × 8 = 2𝜋 cm3 Volume of wire Wire is form of cylinder with radius = r length = height = h = 18 m = 18 × 100 = 1800 cm Volume of wire = 𝜋𝑟2ℎ = 𝜋𝑟2×1800 = 1800𝜋𝑟2 cm2 Now, Volume of copper rod = Volume of wire 1800𝜋𝑟2=2𝜋 1800𝑟2=2 r2 = 2/1800 r2 = 2/1800 r2 = 1/900 r = √(1/900) r = √(1/(30 × 30)) r = √(1/〖30〗^2 ) r = 1/30 So, r = 1/30 cm ∴ Thickness of wire = Diameter of wire = 2r = 2 ×1/30 = 1/15 cm