Let's analyze the question: **Question:** A pipe of diameter 100 mm is to be replaced with 10 pipes of smaller diameter d. The approximate value of the smaller diameter d is: **Options:** - 90 mm - 50 mm - 80 mm - 40 mm ### Solution: The **area of the original pipe** (A1) is: \[ A_1 = \frac{\pi}{4} (100)^2 \] The **area of one smaller pipe** (A2) is: \[ A_2 = \frac{\pi}{4} d^2 \] The **total area of 10 smaller pipes** is: \[ 10 \times A_2 = 10 \times \frac{\pi}{4} d^2 \] For equivalent flow (assuming the same velocity), the total area should be the same: \[ \frac{\pi}{4} (100)^2 = 10 \times \frac{\pi}{4} d^2 \] Cancel \(\frac{\pi}{4}\) from both sides: \[ (100)^2 = 10d^2 \] \[ 10000 = 10d^2 \] \[ d^2 = 1000 \] \[ d = \sqrt{1000} \] \[ d \approx 31.62 \text{ mm} \] ### Closest Option: The closest value to 31.62 mm is **40 mm**. --- **Final Answer:** **40 mm**