Question

The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{frustum},h=6\mathrm{cm}, \\ \mathrm{Radii}\mathrm{of}\mathrm{the}\mathrm{circular}\mathrm{ends},R=14\mathrm{cm}\mathrm{and}r=6\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{frustum}\mathrm{be}l. \\ \mathrm{Now}, \\ l=\sqrt{{\left(R-r\right)}^2+h^2} \\ =\sqrt{{\left(14-6\right)}^2+6^2} \\ =\sqrt{8^2+6^2} \\ =\sqrt{64+36} \\ =\sqrt{100} \\ =10\mathrm{cm} \end{gathered}$$

So, the slant height of the frustum is 10 cm.