Over the years, the **CAT Exam** is known for testing students on the basic-level quant questions. This is a very simple question from **Geometry ** that requires a strong foundation of the concepts of circles and quadrilaterals. For more such questions from CAT Previous Year paper, visit **2IIM's CAT Question Bank**.

Question 6 : From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is

- 88 + 12π
- 80 + 16π
- 86 + 8π
- 82 + 24π

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Given that ABCD be the rectangle of area of 768 sq cm. A semicircular part with diameter AB and area 72π sq cm is removed

From the area given we can find the radius r as

\\frac{πr^2}{2}) = 72π

r^{2} = 144

r = 12 cm

The diameter AB is 24 since r = 12

So we have a rectangle ABCD

AB × BC = 768

24 × BC = 768

BC = \\frac{768}{24})

BC = 32

Now we have to find the perimeter of the left over portion (shaded area)

Perimeter = AD + DC + BC + \\frac{1}{2}) perimeter of the circle

Perimeter = 32 + 24 + 32 + \\frac{2πr}{2}) (r = 12 cm)

Perimeter = 88 + 12π cm

The perimeter of the leftover portion, in cm, is 88 + 12π

The question is **"From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72π sq cm is removed. The perimeter of the leftover portion, in cm, is"**

Choice A is the correct answer.

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