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Grade 99 grade maths

A cone a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes

Profile image of Gopika Babu
9 Years agoGrade 9
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1 Answer

Profile image of Manan Jain
9 Years ago
We know that all the three figures-cone,hemisphere and cylinder are on same base. It means that they will have the same base radius.
so, let the common radius of all figures be ‘r’.
also they have same height.
so, let the common heights of the three figures be ‘h’.
 
Now, volume of hemisphere=\frac{2}{3}\pi r^{3}
                 volume of cylinder=\pir2h
                 volume of cone=\frac{1}{3}\pi r^{2}h
 
so, volume of cone:volume of cylinder:volume of hemisphere=\frac{2}{3}\pi r^{3}:\pir2h:\frac{1}{3}\pi r^{2}h
 
{{(Cancel out the common values)}}
                                                                                         =\frac{2}{3}r\pi×r×r:\pir×r×h:\frac{1}{3}\pir×r×h
                                                                                         =\frac{2}{3}r:h:\frac{1}{3}h
we know that in a hemisphere, radius=height of hemisphere,
so,
                                                                                          =\frac{2}{3}h:h:\frac{1}{3}h
                                                                                          =\frac{2}{3}:1:\frac{1}{3} 
multiply the ratio by 3,we get
                                                                                          =2:3:1
                                                              Thus, the answer is 2:3:1

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