The given figure shows a bucket. A cubical tank can be fully filled by exactly 5 such buckets full of water. What is the length of the cubical water tank?

Let the length of the tank be a.

It is given that the tank can be fully filled with exactly 5 buckets full of water.

Therefore, volume of the tank = 5 × volume of a bucket

The given bucket is in the shape of a frustum of a cone.

It is known that the volume of a frustum of a cone = $\frac{1}{3}\mathrm{\pi h}\left({{\mathrm{r}}_1}^2+{{\mathrm{r}}_2}^2+{\mathrm{r}}_1{\mathrm{r}}_2\right)$, where r₁ and r₂ are the radii of the ends of the frustum, and h is its height.

Therefore, the volume of the bucket

$=\frac{1}{3}\times \frac{22}{7}\times 35\times \left(8^2+{20}^2+8\times 20\right)$

$=\frac{110}{3}\times \left(64+400+160\right)$

$=\frac{110}{3}\times 624$

$=22880 {\mathrm{cm}}^3$

Therefore, volume of the tank = 5 × 22880 cm³

∴ a³ = 114400 cm³                   [∵ Volume of cube = (side)³]

$\Rightarrow a=\sqrt[3]{114400} \mathrm{cm}$

$\Rightarrow a=2\sqrt[3]{14300} \mathrm{cm}$