1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
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
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
r
√
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2
r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
√
3
r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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
.
Suggest Corrections
0
Similar questions
Q.
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius
R
is
2
R
√
3
. Also, find the maximum volume of the cylinder.
Q.
Prove that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius
R
is
2
R
√
3
. Also find the maximum volume.
Q.
Show that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is
2
R
√
3
Also find the maximum volume.
Q.
Show that the height of the cylinder of maximum volume that can be inscribed a sphere of radius R is
2
R
3
.
Q.
Show that when curve surface of a cylinder inscribed in a sphere of radius
r
is maximum, then height of the cylinder is
√
2
r
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
MATHEMATICS
Watch in App
Explore more
Volume and Surface Area of Different Shapes
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app