CAT 2018 Slot 2 — QA Question 19
Basics of Mensuration/PrismEasy
From a rectangle ABCD of area 768 sqcm, a semicircular part with diameter AB and area 72π sqcm is removed. The perimeter of the leftover portion, in cm, is:
Answer & solution
88 + 12π
- B
82 + 24π
- C
80 + 16π
- D
86 + 8π
Solution
The area of the semicircle = 72π sq. cm. If ‘r’ is the radius of the semi-circular portion removed,
We get
Therefore r = 12 cm.
Therefore the diameter of the semi-circle = AB = 24 cm.
Area of rectangle ABCD = 768 sq. cm.
Therefore the length of side AC
The perimeter of the leftover portion
= Perimeter of the semicircle + l(AD) + l(DC) + l(CB)
= 12π + 32 + 24 + 32 = 88 + 12π
Hence, option (a).