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  • A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.

Direction: Write True or False and justify your answer in each of the following :

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.

Answers (1)

Answer: True

We have been given that a cone, a hemisphere and a cylinder stand on equal bases and have the same height.

 Let radius of base is r and height is h.

 Now we know that

Volume of cone,                            V_{Cone}=\frac{1}{3}\pi r^{2}h\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; ....(i)

Volume of hemisphere,                  V_{Hemisphere}=\frac{2}{3}\pi r^{2}h\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; ....(ii)

Volume of cylinder,                        V_{Cylinder}=\pi r^{2}h\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; ....(iii)

From equations (i) (ii) and (iii)

V_{Cone}:V_{Hemisphere}:V_{Cylinder}

=\frac{1}{3}\pi r^{2}h:\frac{2}{3}\pi r^{2}h:\pi r^{2}h

=\frac{1}{3}:\frac{2}{3}:1

=1:2:3

Thus the statement is true.

Posted by

infoexpert23

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