Bodhee Prep-CAT Online Preparation

CAT 2018 [SLOT 2] Quant Question with Solution 30

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

  1. 80 + 16π
  2. 86 + 8π
  3. 82 + 24π
  4. 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+\(\pi ×24/2\)

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


CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2018 Slot-1


CAT 2018 Slot-2


CAT Quant Questions with Video Solutions

30 must do CAT Quant Questions with Video Solutions

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon