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Byju's Answer
Standard XII
Mathematics
Volume and Surface Area of Different Shapes
A cylinder is...
Question
A cylinder is inscribed in a sphere of radius r.
What is the height of the cylinder of maximum volume?
A
2
r
√
3
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B
r
√
3
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C
2
r
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D
√
3
r
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Solution
The correct option is
A
2
r
√
3
We know that volume of the cylinder
V
=
π
(
r
a
d
i
u
s
)
2
×
(
h
e
i
g
h
t
)
here radius is r then
⇒
π
r
2
−
3
4
×
π
h
2
=
0
⇒
3
4
×
π
h
2
=
π
r
2
⇒
h
2
=
π
r
2
3
4
π
⇒
h
=
√
4
r
2
3
⇒
h
=
2
r
√
3
.
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