CAT 2018 Quant Questions

Question:
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

80 + 16π
86 + 8π
82 + 24π
88 + 12π
Show Answer
Correct Answer: 4

Area of the semicircle with AB as a diameter = \(\frac{1}{2}*\pi *(\frac{{A{B^2}}}{4})\)

\( \Rightarrow \) \(\frac{1}{2}*\pi *(\frac{{A{B^2}}}{4})\) = \(72*\pi \)

\( \Rightarrow \) \(AB = 24cm\)

Given that area of the rectangle ABCD = 768 sq.cm

\( \Rightarrow \) AB*BC = 768

\( \Rightarrow \) BC = 32 cm

>

We can see that the perimeter of the remaining shape = AD + DC + BC + Arc(AB)

\( \Rightarrow \) 32+24+32+\(\pi *24/2\)

\( \Rightarrow \) \(88 + 12\pi \)

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CAT 2018 Quant Questions
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