Question
Quantitative Aptitude Question on Mensuration
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
A
80+16π
B
86+8π
C
82+24π
D
88+12π
Answer
88+12π
Explanation
Solution
Area of the semicircle with AB as a diameter = 1/2×π×(AB2/4)
⇒ 1/2×π×(AB2/4) = 72×π
⇒ AB = 24 cm
It is also know that the area of the rectangle ABCD = 768 sq.cm
⇒ AB×BC = 768
⇒ BC = 32cm
Observe that the perimeter of the remaining shape = AD + DC + BC + Arc(AB)
⇒ 32+24+32+π×24/2
⇒ 88 + 12π