Question

Choose the correct answer of the following question:

If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm, then its slant height is

(a) 20 cm (b) $12\sqrt{5}$ cm (c) $8\sqrt{13}$ cm (d) 16 cm [CBSE 2013C]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{frustum},h=16\mathrm{cm}, \\ \mathrm{Radii}\mathrm{of}\mathrm{the}\mathrm{circular}\mathrm{ends},R=\frac{40}{2}=20\mathrm{cm}\mathrm{and}r=\frac{16}{2}=8\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{The}\mathrm{slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{frustum},l=\sqrt{{\left(R-r\right)}^2+h^2} \\ =\sqrt{{\left(20-8\right)}^2+{16}^2} \\ =\sqrt{{12}^2+{16}^2} \\ =\sqrt{144+256} \\ =\sqrt{400} \\ =20\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (a).