Question

A 20 m deep well with a diameter of 7 m is dug, and the soil from digging is evenly spread out to form a platform of 22 m × 14 m. Find the height of the platform.

Hint:

Volume before and after digging remains the same, apply volume conservation.

Answer 1

The volume of soil removed from the well:
\[ V_{\text{well}} = \pi r^2 h. \] \[ = \pi \times \left(\frac{7}{2}\right)^2 \times 20. \] \[ = \pi \times \frac{49}{4} \times 20 = 245\pi. \] The volume of the platform:
\[ V_{\text{platform}} = \text{Base Area} \times \text{Height}. \] \[ = (22 \times 14) \times h. \] \[ = 308h. \] Since soil volume remains constant:
\[ 245\pi = 308h. \] Approximating \( \pi = 3.14 \):
\[ 245 \times 3.14 = 769.3. \] \[ h = \frac{769.3}{308} \approx 2.5 \text{ m}. \]