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  • A cone and a cylinder are having the same base . Find the ratio of their heights if their volumes are equal .

A cone and a cylinder are having the same base . Find the ratio of their heights if their volumes are equal .

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Solution:  Let the radius of the common base be r . Let h_1 and h_2 be the heights of the cone and cylinder respectively . Then ,

                 Volume of the cone 

                                     =frac13pi r^2 h_1 ,

                Volume of the cylinder =pi r^2h_2

It is given that the cone and the cylinder are of the same volume .

herefore              frac13 pi r^2 h_1=pi r^2 h_2Rightarrow frac13h_1=h_2

Rightarrow           frach_1h_2=frac31Rightarrow h_1:h_2=3:1

Hence , the ratio of the height of the cone and cylinder is 3:1.

Posted by

Deependra Verma

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