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Question
A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
Solution 1
Given that
Volume of thee cone = Volume of the hemisphere
⇒`1/3πr^2h=2/3πr^3`
⇒`r^2h=2r^3`
⇒`h=2R`
⇒`h/r=1/1×2=2/1`
∴ Ratio of the their height is 2 :1
Solution 2
Given that
A cone and a hemisphere have equal bases and volumes
`V_"cone" = V _"hemisphere"`
⇒ `1/3πr^2h=2/3πr^3`
⇒`r^2h=2r^3`
⇒`h=2r`
⇒`h:r -2r:r-2:1`
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