A cylindrical storage tank with a 105 ft diameter and 32.5 ft height is filled to 10%. If 12.5% sodium hypochlorite solution is used, approximately how many gallons are needed?

• A. 83
• B. 80
• C. 84
• D. 81

Answer: (C)

The test taps into two ideas at once: how to find the volume of liquid in a partially filled cylinder, and how to estimate a stock chemical dose to reach a target concentration in a large volume of water.

First, find the volume of liquid in the tank. The tank is a cylinder with diameter 105 ft, so the radius is 52.5 ft. It’s filled to 10% of the height, so the liquid height is 3.25 ft. The liquid volume in cubic feet is V = π × r^2 × h = π × (52.5)^2 × 3.25 ≈ 28,100 ft^3. Converting to gallons (1 ft^3 ≈ 7.4805 gal) gives about 210,000 gallons of liquid.

To dose this water with a 12.5% sodium hypochlorite solution to a practical disinfection target, use the mixing approach. A rough estimate for the available chlorine concentration in that stock solution is about 60,000–65,000 mg/L (12.5% NaOCl, with typical density giving roughly 5.9% available chlorine by weight, translating to tens of thousands of mg per liter). Suppose we aim for a final chlorine concentration of around 25 mg/L in the tank (a common shock-chlorination target). If C_stock ≈ 65,000 mg/L and the tank volume V ≈ 795,000 L (210,000 gal × 3.785 L/gal), the required volume x of stock is given by:

x = (C_f × V) / (C_stock − C_f) = (25 × 795,000) / (65,000 − 25) ≈ 306 L ≈ 81 gallons.

Rounding to practical values and considering slight variations in stock concentration, the amount is about 80–85 gallons. The closest answer is around 84 gallons.