a cylinder, a cone and a hemisphere have same base and same height. find the ratio of their volumes
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Volume of hemisphere = 2/3 π r³ = V1
Volume of cylinder = π r²H = V2
Volume of Cone = ⅓ π r² H = V3
We know that radius of hemisphere is its height which means that radius of all given solids are equal to their height since their radius are also given equal.
V1/V2/V3=2/3*π H³ (since r=h) / π H³ / 1/3*π H³
=> 2/3 /1 / 1/3
=>2/3:1:1/3
=> 1:1/3:2/3
Multiplying by 3
=> 3:1:2 is the ratio of volumes of cylinder : Cone : hemisphere
Volume of cylinder = π r²H = V2
Volume of Cone = ⅓ π r² H = V3
We know that radius of hemisphere is its height which means that radius of all given solids are equal to their height since their radius are also given equal.
V1/V2/V3=2/3*π H³ (since r=h) / π H³ / 1/3*π H³
=> 2/3 /1 / 1/3
=>2/3:1:1/3
=> 1:1/3:2/3
Multiplying by 3
=> 3:1:2 is the ratio of volumes of cylinder : Cone : hemisphere
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