CAT 2018 Question Paper Shift 2 Solved Paper

Question : 87 of 100

Marks: +1, -0

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
Options

86 + 8π
80 + 16π
82 + 24π
88 + 12π

Validate

Solution:

Area of the semicircle with

{AB}

as a diameter

=\;{1}/{2} × π ×(\;{A B^{2}}/{4})

⇒ \;{1}/{2} × π ×(\;{A B^{2}}/{4})=72 × π

⇒ A B=24 {cm}

It is also know that the area of the rectangle

{ABCD}=768 {sq.cm}

⇒ {AB} × {BC}=768

⇒ {BC}=32 {cm}

Observe that the perimeter of the remaining shape

= {AD}+ {DC}+ {BC}+\Arc( {AB})

⇒ 32+24+32+π × 24 / 2

⇒ 88+12 π

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