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  • A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone.

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

A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total  surface area of the combined solid is \pi r\left [ \sqrt{r^{2}+h^2}+3r+2h \right ]

Answers (1)

It is given that there is a cone of radius r and height h and a cylinder of height h and radius r.

            

            Where A is placed on B

            

            Total surface area = Surface area of cone + Total surface area of cylinder – Surface area of part I – the surface area of part II

                        =\pi r (r +l)+2\pi r(r+h)-\pi r^{2}- \pi r^{2}

                        = \pi r (r +\sqrt{r^2 +h^2})+2 \pi r (r+h)-2\pi r ^2 (QI= \sqrt{r^2 +h^2})

                        = \pi r (r +\sqrt{r^2 +h^2}+2r+2h -2r)

                        = \pi r (r +\sqrt{r^2 +h^2}+r+2h )

            Total surface area is not equal to

\pi r\left [ \sqrt{r^{2}+h^2}+3r+2h \right ]

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