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A Cone and a Hemisphere Have Equal Bases and Equal Volumes. Find the Ratio of Their Heights. - CBSE Class 9 - Mathematics

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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
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` 

Solution 2

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

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Solution A Cone and a Hemisphere Have Equal Bases and Equal Volumes. Find the Ratio of Their Heights. Concept: Volume of a Sphere.
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