A cone, a hemisphere and a cylinder stand on equal bases of radius and have equal heights .Prove that their volumes are in the ratio . - Padhle.Online
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A cone, a hemisphere and a cylinder stand on equal bases of radius and have equal heights .Prove that their volumes are in the ratio .

 Solution

A cone, a hemisphere and a cylinder stand on equal bases of radius r and have equal heights h.

We have to prove that their volumes are in the ratio 1 : 2 : 3.

From the formula, we have learnt that

Volume of cylinder = πr2hVolume of cone = 13πr2hVolume of hemisphere = 23πr3

Given that the cone, hemisphere and cylinder have an equal base and same height
i.e. r=h

Volume of cone : Volume of hemisphere : Volume of cylinder13πr2h : 23πr3 : πr2h13 : 23 : 11 : 2 : 3

Hence, the ratio of the volume of the cone, hemisphere and cylinder is 1 : 2 : 3.


Mathematics

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Principal, Babu Daudayal SVM, Mathura

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