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CAT 2020 Exam Shift 1 Solved Paper
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© examsnet.com
Question : 54
Total: 76
On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is
5
√
π
(
3
+
9
π
)
3
√
π
(
5
2
+
6
π
)
3
√
π
(
5
+
12
π
)
4
√
π
(
3
+
9
π
)
Validate
Solution:
Let the length and the breadth of the rectangle be 1 and b respectively.
As the circle touches the two opposite sides, its diameter will be same as the breadth of the rectangle. Given,
l
b
=
135
and
l
b
=
π
(
b
2
)
2
=
2
3
×
π
(
b
2
)
2
⇒
5
3
π
(
b
2
4
)
=
135
⇒
b
=
18
√
π
From this
l
=
15
√
π
2
∴
Required perimeter:
2
(
l
+
b
)
=
2
[
15
√
π
2
+
18
√
π
]
=
3
√
π
[
5
2
+
6
π
]
© examsnet.com
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