The question states: **"A pipe of diameter 100 mm is be replaced with 10 pipes of smaller diameter d. The approximate value of the smaller diameter d is"** This is a problem involving the conservation of cross-sectional area: \[ \text{Area of larger pipe} = \text{Total area of smaller pipes} \] Mathematically: \[ \pi \left(\frac{D}{2}\right)^2 = 10 \times \pi \left(\frac{d}{2}\right)^2 \] Canceling \(\pi\): \[ \left(\frac{D}{2}\right)^2 = 10 \times \left(\frac{d}{2}\right)^2 \] \[ \left(\frac{D}{2}\right)^2 = 10 \times \left(\frac{d}{2}\right)^2 \] \[ D^2 / 4 = 10 \times d^2 / 4 \] Multiply both sides by 4: \[ D^2 = 10 \times d^2 \] Given \( D = 100\, \text{mm} \): \[ (100)^2 = 10 \times d^2 \] \[ 10,000 = 10 \times d^2 \] \[ d^2 = \frac{10,000}{10} = 1,000 \] \[ d = \sqrt{1,000} \approx 31.62\, \text{mm} \] **Closest approximate value among options:** - 40 mm - 50 mm - 90 mm - 80 mm **Answer: 40 mm** --- ### **Correct option: 40 mm**