Minnesota Boiler License Practice Exam

How many gallons can a tank hold if it has the dimensions of 110 feet high and 90 feet in diameter, filled 70%?

1. 45,000 gallons

2. 47,688.75 gallons

3. 50,500 gallons

4. 55,000 gallons

The correct answer is: 47,688.75 gallons

To find out how many gallons a tank can hold, especially when it's filled to a certain percentage, it's important first to calculate the volume of the tank in cubic feet, and then convert that volume into gallons. The formula for the volume of a cylinder is: \[ V = \pi r^2 h \] Where: - \( V \) is the volume, - \( r \) is the radius, - \( h \) is the height. Given the tank's height is 110 feet and the diameter is 90 feet, we can find the radius by dividing the diameter by 2: \[ r = \frac{90}{2} = 45 \text{ feet} \] Now substituting \( r \) and \( h \) into the volume formula: \[ V = \pi (45)^2 (110) \] Calculating this step-by-step: 1. Calculate \( (45)^2 = 2025 \). 2. Multiply by the height: \( 2025 \times 110 = 222750 \). 3. Finally multiply by \( \pi \) (approximately 3.14159): \[ V \approx 3.14159 \times 222750 \approx