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  • The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Figure is

Write ‘True’ or ‘False’ and justify your answer in the following:

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Figure is \frac{\pi r^{2}}{3}[3h-2r]

 

Answers (1)

AnswerTrue

Solution

            It is given that a cylindrical vessel of height h and radius r is raised upward with a hemispherical portion.

            From the figure radius of hemisphere = r cm

            The volume of the figure = volume of the cylinder – the volume of the hemisphere

                        =\pi r^{2}h - \frac{2}{3}\pi r^{3}

                        =\pi r^{2}\left [h-\frac{2}{3}r \right ]

                        =\pi r^{2}\left [\frac{3h -2r}{3} \right ]

                        =\frac{\pi r^{2}}{3}[3h-2r]

\text{ Hence the capacity of the vessel is }\frac{\pi r^{2}}{3}[3h-2r]

So the given statement is True.

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