# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Mensuration Questions | Question 6

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

1. 88 + 12π
2. 80 + 16π
3. 86 + 8π
4. 82 + 24π

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##### Method of solving this CAT Question from Mensuration

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
$$frac{πr^2}{2}$ = 72π r2 = 144 r = 12 cm The diameter AB is 24 since r = 12 So we have a rectangle ABCD AB × BC = 768 24 × BC = 768 BC = $\frac{768}{24}$ BC = 32 Now we have to find the perimeter of the left over portion$shaded area)
Perimeter = AD + DC + BC + $$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"

##### Hence, the answer is 88 + 12π cm

Choice A is the correct answer.

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