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 = \(\frac{1}{2}×\pi ×(\frac{{A{B^2}}}{4})\)

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

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

It is also know that the area of the rectangle ABCD = 768 sq.cm

\( \Rightarrow \) AB×BC = 768

\( \Rightarrow \) BC = 32 cm

Observe that the perimeter of the remaining shape = AD + DC + BC + Arc(AB)

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

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


Get one day FREE Trial of CAT online Full course FREE Registration
Also Check: 841+ CAT Quant Questions with Solutions


CAT Quant Online Course


  • 1000+ Practice Problems
  • Detailed Theory of Every Topics
  • Online Live Sessions for Doubt Clearing
  • All Problems with Video Solutions
₹ 2999

CAT 2018 Questions Paper with Solution PDF Download


CAT 2018 Quant Questions with Solutions

CAT 2018 Slot-1


CAT 2018 Slot-2


Back to Main Page



Try CAT 2020 online course for 1 day for FREE

Please provide your details to get FREE Trial of Bodhee Prep's Online CAT Course for one day. We will inform you about the trial on your whatsApp number with the activation code.