Question

The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area.
[Use $\mathrm{\pi }$ = 3.14] [CBSE 2011]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height},h=8\mathrm{cm}, \\ \mathrm{Base}\mathrm{radii},R=18\mathrm{cm}\mathrm{and}r=12\mathrm{cm} \\ \mathrm{Also},\mathrm{the}\mathrm{slant}\mathrm{height},l=\sqrt{{\left(R-r\right)}^2+h^2} \\ =\sqrt{{\left(18-12\right)}^2+8^2} \\ =\sqrt{6^2+8^2} \\ =\sqrt{36+64} \\ =\sqrt{100} \\ =10\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{frustum}=\mathrm{\pi }\left(R+r\right)l+\mathrm{\pi }{R}^2+\mathrm{\pi }{r}^2 \\ =3.14\times \left(18+12\right)\times 10+3.14\times {18}^2+3.14\times {12}^2 \\ =3.14\times 30\times 10+3.14\times 324+3.14\times 144 \\ =3.14\times \left(300+324+144\right) \\ =3.14\times 768 \\ =2411.52{\mathrm{cm}}^2 \end{gathered}$$

So, the total surface area of the solid frustum is 2411.52 cm².