A solid cone of radius r and height h


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

thecombined solid is $\left[\sqrt{r^{2}+h^{2}}+3 r+2 h\right]$.



We know that, total surface area of a cone of radius, r

and $\quad$ height, $h=$ Curved surface Area $+$ area of base $=\pi r l+\pi r^{2}$

where, $l=\sqrt{h^{2}+r^{2}}$

and total surface area of a cylinder of base radius, $r$ and height, $h$

$=$ Curved surface area + Area of both base $=2 \pi r h+2 \pi r^{2}$

Here, when we placed a cone over a cylinder, then one base is common for both. So, total surface area of the combined solid

$=\pi r l+2 \pi r h+\pi r^{2}=\pi r[l+2 h+r]$

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


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