Question

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water . The radii of the top and bottom are 28 cm and 21 cm respectively . Find the height of the bucket .

Answer 1

Radii r₁ = 21 cm and r₂ = 28 cm
Let the height of the bucket be h.
Volume of the bucket which is in the form of the frustum
$$\begin{gathered} V=\frac{1}{3}\mathrm{\pi h}\left({\mathrm{r}}_1^2+{\mathrm{r}}_1{\mathrm{r}}_2+{\mathrm{r}}_2^2\right) \\ \Rightarrow \frac{1}{3}\mathrm{\pi h}\left({28}^2+28\times 21+{21}^2\right)=28490 \\ \Rightarrow \mathrm{h}=14.9\approx 15\mathrm{cm} \end{gathered}$$
Hence, the height of the bucket is 15 cm.