A bucket is in the form of a frustum of a cone and its can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. $\left[\mathrm{use} \mathrm{\pi } = \frac{22}{7}\right]$

Here, R = 28 cm  and  r = 21 cm, we need to find h

Volume of frustum = 28.49 L = 28.49 x 1000 cm³ = 28490 cm³

Now, volume of frustum =  $\frac{\mathrm{\pi h}}{3} \left({\mathrm{R}}^2 + \mathrm{Rr} + {\mathrm{r}}^2\right)$

$$\begin{gathered} \Rightarrow \frac{22\mathrm{h}}{7 \mathrm{x} 3}\left({28}^2 + 28 \mathrm{x} 21 + {21}^2\right) = 28490 \\ \Rightarrow \frac{22}{21}\mathrm{h} \mathrm{x} 1813 = 28490 \\ \Rightarrow \mathrm{h} = \frac{28490 \mathrm{x} 21}{22 \mathrm{x} 1813} \\ = 15 \mathrm{cm} \end{gathered}$$

Hence the height of bucket is 15 cm.