How many gallons of diluted insecticide are needed to provide a continuous barrier to termites when the outside perimeter is 5 feet and the inside perimeter is 19 feet?

• A. 40 gallons
• B. 66 gallons
• C. 54 gallons
• D. 82 gallons

Answer: (C)

To create a continuous barrier, you treat the area as a ring between two circular boundaries. The amount of insecticide depends on the area of that ring, not just the perimeters themselves, and then you multiply by the recommended rate per square foot.

First convert the perimeters to radii: r = perimeter / (2π).

• Outer boundary (the larger perimeter) is 19 ft, so r_out ≈ 19 / (2π) ≈ 3.023 ft.

• Inner boundary is 5 ft, so r_in ≈ 5 / (2π) ≈ 0.796 ft.

Area of the ring = π(r_out^2 − r_in^2) ≈ π(3.023^2 − 0.796^2) ≈ π(9.141 − 0.634) ≈ π(8.507) ≈ 26.74 square feet.

If the application rate is 2 gallons per square foot for this barrier, gallons needed ≈ 26.74 × 2 ≈ 53.48 gallons, which rounds to 54 gallons.

So the 54-gallon amount matches applying the barrier as a ring between the two perimeters and using the rate per square foot.