The radii of ends of a frustum are $14\ cm$ and $6\ cm$ respectively and its height is $6\ cm$. Find its total surface area.


Given: The radii of ends of a frustum are $14\ cm$ and $6\ cm$ respectively and its height is $6\ cm$.

To do: To find its total surface area.

Solution:

As given, Radius of the lower end $R=14\ cm$,  radius of the upper end, $r=6\ cm$, height of the  frustum, $h=6\ cm$.

$\therefore$ Slant height of the frustum, $l=\sqrt{h^2+( R-r)^2}$

$\Rightarrow l=\sqrt{6^2+( 14-6)^2}$

$\Rightarrow l=\sqrt{36+64}$

$\Rightarrow l=\sqrt{100}$

$\Rightarrow l=10\ cm$ 

$\therefore$ Curved surface area of the frustum$=\pi ( r+R)l$

$=3.14\times( 14+6)\times 10$

$=628\ cm$

Thus, the curved surface area of the frustum is $628\ cm$.

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Updated on: 10-Oct-2022

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