Questions: The Salt Farmers' Guild has decided to process the waste water produced in the region. Gulbarga Cactus trees have been planted, the most widely used indigenous plant for wastewater treatment in semi-arid regions. The Guild planted 1,000 trees in a circular plantation. The plantation site is 100 feet in diameter. The trees are spaced 3 feet apart on the circumference of the circle. Each tree requires 5 gallons of water per day. What is the minimum number of trees required to process all the wastewater?

Solution Steps

1. Calculate the circumference of the circular plantation using the formula \( C = \pi \times \text{diameter} \).
2. Determine the number of trees that can be planted on the circumference by dividing the circumference by the spacing between the trees.
3. Calculate the total water requirement for all the trees by multiplying the number of trees by the water requirement per tree.
4. Determine the minimum number of trees required to process all the wastewater by dividing the total water requirement by the water processed by each tree.

The circumference \( C \) of the circular plantation is calculated using the formula: \[ C = \pi \times \text{diameter} = \pi \times 100 \approx 314.1593 \text{ feet} \]

The number of trees \( N \) that can be planted on the circumference is given by: \[ N = \frac{C}{\text{spacing}} = \frac{314.1593}{3} \approx 104.0 \]

The total water requirement \( W \) for all the trees is: \[ W = N \times \text{water per tree} = 104.0 \times 5 = 520.0 \text{ gallons per day} \]

Since each tree processes 5 gallons of wastewater per day, the minimum number of trees required \( M \) to process all the wastewater is: \[ M = \frac{W}{\text{water per tree}} = \frac{520.0}{5} = 104.0 \]

Final Answer