MathDB
Problems
Contests
International Contests
IMO Shortlist
1966 IMO Shortlist
21
21
Part of
1966 IMO Shortlist
Problems
(1)
Geometry inequality on volume and area
Source:
9/27/2010
Prove that the volume
V
V
V
and the lateral area
S
S
S
of a right circular cone satisfy the inequality
(
6
V
π
)
2
≤
(
2
S
π
3
)
3
\left( \frac{6V}{\pi}\right)^2 \leq \left( \frac{2S}{\pi \sqrt 3}\right)^3
(
π
6
V
)
2
≤
(
π
3
2
S
)
3
When does equality occur?
geometry
3D geometry
area
Volume
geometric inequality
IMO Longlist
IMO Shortlist