For obtaining a cup of diameter 25 mm and height 15 mm by drawing, the size of the round blank should be approximately

Solution (By Examveda Team)

The correct answer is (C) 46 mm.

Here's why: In drawing operations, we start with a flat, round piece of metal (the blank) and form it into a desired shape, like a cup. To determine the initial blank size, we need to consider that the volume of material remains approximately constant during the drawing process.

Imagine flattening out the cup. The area of that flattened-out material (the blank) must equal the surface area of the finished cup.

A simplified way to estimate this for a cylindrical cup is:
1. Calculate the surface area of the cup (bottom circle + side wall).

* Area of the bottom circle: π * (diameter/2)^2 = π * (25/2)^2 ≈ 490.87 mm²
* Area of the side wall: π * diameter * height = π * 25 * 15 ≈ 1178.10 mm²
* Total surface area ≈ 490.87 + 1178.10 = 1668.97 mm²
2. Calculate the blank diameter : the area of the blank circle is equal to the total surface area of the cup. * Area of the blank circle = π * (diameter/2)^2 * π * (diameter/2)^2 = 1668.97 mm² * diameter/2= sqrt(1668.97/π) = 23.05 * diameter = 2 * 23.05 = 46.1 mm
Therefore, the blank size is approximately 46 mm. In practice, a few more factors might influence the *exact* size (like material properties and thinning during drawing), but this gives a good estimate.