A cone, a hemisphere and a cylinder standing on same and have same height. Find the ratio of their volumes.
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Let r and h be the radius of base and height of the cylinder, cone and hemisphere.
We know that, Height of hemisphere = Radius of the hemisphere
∴ h = r
Volume of cylinder = πr2h = πr2 × r = πr3
Volume of cone = 1/3 (pie) r^3
Volume of hemisphere = 2/3(pie)r^3
Volume of cylinder : Volume of cone : Volume of hemisphere
(Pie)r^3: 1/3(pie)r^3: 2/3(pie)r^3
Thus, the ratio of their volumes is 3 : 1 : 2.
We know that, Height of hemisphere = Radius of the hemisphere
∴ h = r
Volume of cylinder = πr2h = πr2 × r = πr3
Volume of cone = 1/3 (pie) r^3
Volume of hemisphere = 2/3(pie)r^3
Volume of cylinder : Volume of cone : Volume of hemisphere
(Pie)r^3: 1/3(pie)r^3: 2/3(pie)r^3
Thus, the ratio of their volumes is 3 : 1 : 2.
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