Question

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminum of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

The proportion of the sheet area that remains after punching is

• A. $\frac{\pi +2}{8}$
• B. $\frac{6-\pi }{8}$
• C. $\frac{4-\pi }{4}$
• D. $\frac{\pi -2}{4}$
• E. $\frac{14-3\pi }{6}$

Answer 1

The correct option is B $\frac{6-\pi }{8}$

Option (B) is the correct answer. Check the video for the approach.