a cone and a hemisphere have equal bases and equal volumes find the ratio of their Heights
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Hey mate..
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Let the height of the hemisphere be h'
Given,
Volume of cone = Volume of a Hemisphere
Thus,
1/3 πr^2h = 2/3 πr^3
=> 1/3 × 3/2 × π × 1/π × r^2 × 1/r^3 = 1/h
=> 1/2 × 1/r = 1/h
=> 2r = h
=> 2 = h/r
=> 2 = h/h' [ °•° Height of the Hemisphere = Radius of the hemisphere ]
=> 2/1 = h/h'
Thus, The required ratio is 2:1
Hope it helps !!
========
Let the height of the hemisphere be h'
Given,
Volume of cone = Volume of a Hemisphere
Thus,
1/3 πr^2h = 2/3 πr^3
=> 1/3 × 3/2 × π × 1/π × r^2 × 1/r^3 = 1/h
=> 1/2 × 1/r = 1/h
=> 2r = h
=> 2 = h/r
=> 2 = h/h' [ °•° Height of the Hemisphere = Radius of the hemisphere ]
=> 2/1 = h/h'
Thus, The required ratio is 2:1
Hope it helps !!
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