If a sump has a top diameter of 16 inches and a bottom diameter of 14 inches, what is the minimum required depth?

• A. 20 inches
• B. 22 inches
• C. 24 inches
• D. 26 inches

Answer: (B)

Think of the sump as a short cone with sloped sides, i.e., a frustum. The depth you need is found by matching the sump’s volume to the required liquid capacity. The top diameter is 16 inches (radius 8) and the bottom diameter is 14 inches (radius 7). For a frustum, V = (π h / 3) (R1^2 + R1 R2 + R2^2). Here that sum is 8^2 + 8·7 + 7^2 = 64 + 56 + 49 = 169, so V = (169π/3) h.

Convert the required capacity to cubic inches. If the minimum capacity is 17 gallons, that’s 17 × 231 = 3927 cubic inches. Set V = 3927 and solve for h:

h = (3 × 3927) / (169π) ≈ 22 inches.

So the minimum depth is about 22 inches. At this depth the sump holds roughly 16.9 gallons, which aligns with selecting the depth nearest to the required capacity in the given options.