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

 Volume of the bucket = 28.490 litres = 28.490 × 1000 = 28490 cm³

The radii of the bucket are 28 cm and 21 cm.

So, r₁ = 28 cm and r₂ = 21 cm

Let the height of the bucket be h cm.

∴ Volume of the frustum $=\frac{\mathrm{\pi h}}{3}\left({{\mathrm{r}}_1}^2+{{\mathrm{r}}_2}^2+{\mathrm{r}}_1{\mathrm{r}}_2\right)$

$\Rightarrow 28490=\frac{\mathrm{\pi h}}{3}\left({28}^2+{21}^2+28\times 21\right)$

$\Rightarrow 28490=\frac{\mathrm{\pi h}}{3}\times 1813$

$\Rightarrow \mathrm{h}=\frac{28490\times 3\times 7}{1813\times 22}$

$\Rightarrow \mathrm{h}=15 \mathrm{cm}$

Therefore, the height of the bucket is 15 cm.