Raised Bed for the Community Garden
A neighborhood group is building one rectangular raised bed measuring 12 ft by 18 ft and filling it to a depth of 4 inches with topsoil. The soil supplier sells 2.0 ft³ bags for $8.50 each and recommends adding 10% extra volume to allow for settling and compaction. Around the bed the group will install 1.5 m fence panels costing $24.50 each; a 0.9 m gate opening will replace part of the fence line, and panels cannot be cut or spliced. A second supplier quotes 50 L bags of the same soil at $11.20 each. The group has one budget for soil and one for fencing and has asked for the quantities before ordering.
1. How much soil is needed, how many bags of the 2.0 ft³ size must be bought, and what will the soil cost?
Read the worked answer
Area: 12 ft × 18 ft = 216 ft².
Depth in feet: 4 in ÷ 12 = 1/3 ft ≈ 0.333 ft.
Volume: 216 × 1/3 = 72 ft³.
With 10% settling allowance: 72 × 1.10 = 79.2 ft³.
Bags: 79.2 ÷ 2.0 = 39.6 → 40 bags (must round up; 39 bags gives only 78 ft³, under the allowance).
Cost: 40 × $8.50 = $340.00.
Judgment note: the 10% allowance itself consumes a whole bag - without it, 36 bags would be exactly 72 ft³ but would leave the bed visibly low after watering and settling.
2. How many 1.5 m fence panels are required, and what is the fencing cost? Watch the units.
Read the worked answer
Perimeter: 2(12 + 18) = 60 ft.
Convert to meters: 60 × 0.3048 = 18.288 m.
Subtract the gate: 18.288 − 0.9 = 17.388 m of fence needed.
Panels: 17.388 ÷ 1.5 = 11.59 → 12 panels.
Cost: 12 × $24.50 = $294.00.
Check: 12 panels cover 18.0 m; 18.0 − 0.9 (gate) = 17.1 m of fence line, which is less than the 17.388 m needed - so verify with the exact figures: 11 panels cover 16.5 m and leave 0.888 m open. Rounding up to 12 is still the right purchase because panels cannot be spliced; the small overage must be absorbed by adjusting the gate position or bed layout. Forgetting to convert feet to meters would give 60 ÷ 1.5 = 40 panels - a $686 over-order.
3. Compare the two soil suppliers on cost per cubic foot and on total cost for this bed. Which should the group buy from?
Read the worked answer
Supplier A (2.0 ft³ bag, $8.50): cost per ft³ = 8.50 ÷ 2.0 = $4.25/ft³. Total for 40 bags = $340.00.
Supplier B (50 L bag, $11.20): convert volume: 50 ÷ 28.3168 = 1.766 ft³ per bag.
- Cost per ft³ = 11.20 ÷ 1.766 = $6.34/ft³.
- Bags needed: 79.2 ÷ 1.766 = 44.85 → 45 bags → 45 × $11.20 = $504.00.
Comparison: Supplier A is cheaper per cubic foot ($4.25 vs. $6.34) and cheaper in total ($340.00 vs. $504.00), a difference of $164.00. Buy from Supplier A.
Judgment: the larger number on the bag label (50 vs. 2.0) is meaningless until units are unified; 50 L is under 2 ft³, so the metric bag is smaller in volume and more expensive per unit of soil.