Question

A copper rod of 200 mm diameter and 400 mm length is extruded to the final diameter of 100 mm. The extrusion ratio is

• A. 1
• B. 2
• C. 4
• D. 8

Hint:

The extrusion ratio is calculated as the ratio of the initial cross-sectional area to the final cross-sectional area.

Answer 1

The Correct Option is C

- The extrusion ratio (ER) is given by the ratio of the initial to final cross-sectional area, i.e., \[ ER = \frac{\text{Initial area}}{\text{Final area}} = \frac{\pi r_1^2}{\pi r_2^2}. \] - Given that the initial diameter $d_1 = 200$ mm and final diameter $d_2 = 100$ mm, we find the radii: $r_1 = 100$ mm and $r_2 = 50$ mm. Substituting these values: \[ ER = \frac{\pi (100)^2}{\pi (50)^2} = \frac{100^2}{50^2} = 4. \] Thus, the correct answer is (C).