CAT 2006 — QA Question 14

Basics of Mensuration/PrismEasy

Passage / Data

Answer the next 2 questions based on the information given below:

A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium 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.

Find the area of the part of the circle (round punch) falling outside the square sheet.

Answer & solution

A
$\frac{π}{4}$
B
$\frac{π - 1}{2}$
C
$\frac{π - 1}{4}$
$\frac{π - 2}{2}$
E
$\frac{π - 2}{4}$

Solution

We have calculated this value while solving the previous question.

The area of part of the circle falling outside the square sheet

= 2 × (Area of sector OPC – Area of âOPC)

$= \frac{π - 2}{2} sq . units$

Hence, option (d).

CAT 2006 QA Q14: Find the area of the part of the circle (round punch) falling outside the square sheet. — Solution | TheCATExam