A 20 m deep well with diameter 7 m is dug up and the earth from digging is spread evenly to form a platform 22 m × 14 m. Determine the height of the platform.

The shape of the deep well will be cylindrical with radius (r) and height (h) = 20 m.

By formula,

Volume of a cylinder = πr²h

r = $\dfrac{\text{diameter}}{2} = \dfrac{7}{2} = 3.5$ m.

Let height of platform be H.

Volume of earth is spread evenly to form a rectangular platform (cuboid).

Volume of platform = 22 m × 14 m × height(H)

Volume of earth dug from well = Volume of earth spread evenly to form a platform

$\Rightarrow π\text{r}^2 \text{ h} = 22 \times 14 \times \text{H} \\[1em] \Rightarrow \dfrac{22}{7} \times (3.5)^2 \times 20 = 308 \times \text{H} \\[1em] \Rightarrow \dfrac{22}{7} \times 12.25 \times 20 = 308 \times \text{H} \\[1em] \Rightarrow \dfrac{5390}{7 \times 308} = \text{H} \\[1em] \Rightarrow \text{H} = \dfrac{5390}{2156} \\[1em] \Rightarrow \text{H} = 2.5 \text{ m.}$

Hence, the height of the platform is 2.5 m.