A cylindrical copper rod of diameter 1 cm and length 8 cm is drawn into a cylindrical wire of length - Maths - Surface Areas and Volumes

Question

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

Harleen Birdi · Accepted Answer

Cylindrical rod: Diameter (D) = 1 cm â‡’ Radius (R) = $\frac{1}{2} cm$ Height of rod (H) = length of rod = 8 cm âˆ´ Volume of rod = Ï€R2H $= π× (\frac{1}{2})^{2} \times 8 {cm}^{3}$ Cylindrical rod is drawn into a cylindrical wire of length (h) 18 m (= 1800 cm) âˆ´ Volume of cylindrical rod = volume of cylindrical wire Let r be the radius of cross-section of the wire $∴ π \times (\frac{1}{2})^{2} \times 8 = π× r^{2} \times 1800 cm \Rightarrow r^{2} = \frac{1}{900} \Rightarrow r = \frac{1}{30} cm \Rightarrow r = \frac{1}{3} mm$ So, the diameter of the cross-section $= \frac{2}{3} mm=0 67 mm$ (approx) Hence, thickness of the wire = 0 67 mm (approx)

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