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
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
Updated On: Sep 30, 2024
- 80+16π
- 86+8π
- 82+24π
- 88+12π
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The Correct Option is D
Solution and Explanation
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
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