Which set of dimensions represents the minimum sump size?

• A. Top 16 inches, Bottom 14 inches, Depth 22 inches
• B. Top 18 inches, Bottom 16 inches, Depth 24 inches
• C. Top 14 inches, Bottom 12 inches, Depth 20 inches
• D. Top 20 inches, Bottom 18 inches, Depth 26 inches

Answer: (A)

Think of the sump’s capacity as the key factor in determining its minimum size. When the opening at the top is larger than the bottom, the sump is like a frustum of a cone. The volume (capacity) is what you use to judge “minimum size,” since a bigger volume holds more water and a smaller volume holds less.

Use the frustum volume formula with top diameter, bottom diameter, and depth: V ≈ (π × depth / 12) × (top^2 + top × bottom + bottom^2). Plugging in the numbers:

• Top 16, bottom 14, depth 22 gives a volume around 3,900 in³ (about 21 gallons).

• Top 18, bottom 16, depth 24 gives about 5,650 in³ (about 30 gallons).

• Top 14, bottom 12, depth 20 gives about 2,660 in³ (about 14 gallons).

• Top 20, bottom 18, depth 26 gives about 7,370 in³ (about 39 gallons).

The smallest capacity is the third set, so that set represents the minimum sump size under this model. If the provided answer differs, the discrepancy likely comes from a different convention or units used in the problem’s source.