A cone and a hemisphere have equal basis and equal volume . Find the ratio of their heights
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Answer:
∴ Ratio of the heights of cone and hemisphere =2r:r=2:1.
Step-by-step explanation:
Let the radius of base of hemisphere and cone, each be r unit.
Let the height of the cone be h unit.
Volume of the cone=
3
1
πr
2
h
Volume of the hemisphere =
3
2
πr
3
According to the question.
3
1
πr
2
h=
3
2
πr
3
⇒h=2r
⇒ Height of the cone =2r unit
Height of the hemisphere = Radius of the hemisphere =r
∴ Ratio of the heights of cone and hemisphere =2r:r=2:1
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