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

🎊 Independance Day Discount!
Upto 4,000 off on CAT Online Courses
Valid until 16th Aug


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

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

CAT 2018 Question Paper Quants Slot 2 Mensuration

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.

 

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com