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Byju's Answer
Standard XII
Mathematics
Volume and Surface Area of Different Shapes
The height of...
Question
The height of a right circular cylinder of maximum volume inscribed in a sphere of radius of
3
is :
A
2
3
√
3
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B
2
√
3
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C
√
6
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D
√
3
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Solution
The correct option is
B
2
√
3
Let
∠
A
O
B
=
θ
and radius of sphere is
r
.
∴
Radius of cylinder
=
r
sin
θ
and Height of cylinder
=
2
r
cos
θ
Volume of cylinder,
V
=
π
(
r
sin
θ
)
2
×
2
r
cos
θ
⇒
V
=
π
2
r
3
sin
2
θ
cos
θ
d
V
d
θ
=
π
2
r
3
(
2
sin
θ
cos
2
θ
−
sin
3
θ
)
For maxima or minima,
d
V
d
θ
=
0
⇒
sin
θ
(
2
cos
2
θ
−
sin
2
θ
)
=
0
⇒
tan
θ
=
√
2
⇒
cos
θ
=
1
√
3
∴
Height of cylinder
=
2
r
cos
θ
=
2
×
3
×
1
√
3
=
2
√
3
Suggest Corrections
0
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Volume and Surface Area of Different Shapes
Standard XII Mathematics
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