Question

A lateral has 12 sprinklers spaced 14 metres apart. The laterals are spaced 20 metres on the main line. Determine the amount of fertilizer to be applied at each setting when the recommended fertilizer dose is 80 kg/ha.

• A. 22 kg
• B. 20 kg
• C. 27 kg
• D. 30 kg

Hint:

To perform this quickly without pen and paper:
\[ 12 \times 14 \times 20 = 3360 \text{ m}^2 \] Multiplying \(3360 \times 80\) is \(268,800\).
Dividing by \(10,000\) yields \(26.88\text{ kg}\), which rounds closest to \(27\text{ kg}\).

Answer 1

The Correct Option is C

Step 1: Find the ground area irrigated by a single sprinkler position.
Each sprinkler effectively waters a rectangular patch of ground defined by the spacing between sprinklers along the lateral and the spacing between adjacent laterals, so the area served by one sprinkler position is \[ 14 \text{ m} \times 20 \text{ m} = 280 \text{ m}^2 \]
Step 2: Scale that up to the full lateral of 12 sprinklers.
Since the lateral carries 12 sprinklers, each covering its own 280 square metre patch side by side, the total ground area wetted during one setting of the lateral is \[ 280 \text{ m}^2 \times 12 = 3360 \text{ m}^2 \]
Step 3: Convert this area into hectares to match the units of the fertilizer dose.
Since 1 hectare equals 10,000 square metres, \[ \frac{3360}{10{,}000} = 0.336 \text{ ha} \]
Step 4: Apply the recommended dose per hectare to this area.
\[ 0.336 \text{ ha} \times 80 \text{ kg/ha} = 26.88 \text{ kg} \approx 27 \text{ kg} \] which matches one of the given choices once rounded to the nearest whole kilogram.
\[ \boxed{27 \text{ kg}} \]