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Standard IX
Mathematics
Question
A sphere is inscribed in a cone of radius
3
√
3
and slant height
6
√
3
. The radius of the sphere is:
3
3
√
3
6
√
3
3
√
3
2
A
3
B
6
√
3
C
3
√
3
2
D
3
√
3
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Solution
Verified by Toppr
D
E
=
D
O
=
radius of sphere
△
A
B
C
is an equilateral
△
, with
D
O
⊥
B
C
. The
△
D
O
B
is a
30
−
60
−
90
triangle & as
B
O
=
O
C
=
3
√
3
O
D
O
B
=
t
a
n
30
0
⇒
O
D
3
√
3
=
1
√
3
⇒
O
D
=
3
∴
Radius of sphere is
3
.
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