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Byju's Answer
Standard XII
Mathematics
Differentiation under Integral Sign
In the figure...
Question
In the figure, semi-circle with center
O
is drawn on
A
B
.
The ratio of the larger shaded area to the smaller shaded area, is
A
4
π
−
2
√
3
2
π
−
2
√
3
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B
3
π
−
2
√
3
2
π
−
2
√
3
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C
4
π
−
3
√
3
3
π
−
3
√
3
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D
4
π
−
3
√
3
2
π
−
3
√
3
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Solution
The correct option is
D
4
π
−
3
√
3
2
π
−
3
√
3
Let
r
be the radius of the semi-circle.
Ratio
=
120
∘
360
∘
π
r
2
−
1
2
r
×
r
sin
(
120
∘
)
60
∘
360
∘
π
r
2
−
1
2
r
×
r
sin
(
60
∘
)
=
120
∘
360
∘
π
r
2
−
1
2
r
2
√
3
2
60
∘
360
∘
π
r
2
−
1
2
r
2
√
3
2
=
4
π
−
3
√
3
2
π
−
3
√
3
Suggest Corrections
3
Similar questions
Q.
In the figure,
P
Q
S
O
is a trapezium in which
P
Q
is parallel to
O
S
,
∠
P
O
S
=
120
∘
and
∠
P
Q
S
=
90
∘
.
Points
P
,
Q
and
R
lie on a circle with center
O
and radius
10.
Then the area of the shaded region, is
Q.
In the figure, a semi-circle with centre
O
is drawn on
A
B
. The ratio of the larger shaded area to the smaller shaded area is ?
Δ
P
B
O
=
60
o
.
Q.
ΔABC is an equilateral triangle of side 14 cm. A semi circle on BC as diameter is drawn to meet AB at D, and AC at E. Find the area of the shaded region.
Q.
In the following figure, If ABC is an equilateral triangle, then shaded area is equal to
(a)
π
3
-
3
4
r
2
(b)
π
3
-
3
2
r
2
(c)
π
3
+
3
4
r
2
(d)
π
3
+
3
r
2
Figure