Determine the ratio of the cone, cylinder, and hemisphere volumes with the same height and circular base. [Answer Limit: 50 words] [UKPSC 2012]
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Determine the ratio of the cone, cylinder, and hemisphere volumes with the same height and circular base. [Answer Limit: 50 words] [UKPSC 2012]
For a cone, hemisphere, and cylinder with the same circular base radius
𝑟
r and height
ℎ
h:
Cone volume:
1
3
𝜋
𝑟
2
ℎ
3
1
πr
2
h
Hemisphere volume:
2
3
𝜋
𝑟
3
3
2
πr
3
Cylinder volume:
𝜋
𝑟
2
ℎ
πr
2
h
The ratio of volumes is
1
:
2
:
3
1:2:3.