Tank & Cylinder Volume
Volumes of cylindrical tanks and pipes - capacity, fill times and dosing.
Why this matters
Where it occurs
Treatment operators calculate tank capacity and detention time; plumbers size water heaters and expansion vessels.
Why calculate it
A tank's capacity drives how long processes have to act - disinfection contact time, settling, heating.
What decision it supports
Is the tank big enough? How long is the detention time? How much chemical is needed per fill?
What happens if it is wrong
A radius-versus-diameter mix-up gives volumes four times too large - or too small for safety-critical contact times.
The concept
The volume of a cylinder is the base area times the height: V = π x r² x h.
Diameter is twice the radius - squaring the diameter instead of the radius inflates volume by a factor of four.
Detention time ties volume to flow: t = V / Q. A 50 m³ tank at 200 m³/h holds water for 15 minutes.
Formula
Cylinder Volume
V = pi x r^2 x h
- V = Volume (m³ or L)
- r = Radius (metres)
- h = Height (metres)
Worked example
Problem: A cylindrical tank has radius 0.75 m and height 3 m. What is its capacity?
- Use V = π x r² x h.
- Substitute: V = 3.1416 x 0.75² x 3.
- Calculate: V = 3.1416 x 0.5625 x 3 = 5.3 m³.
- Convert: 5300 L.
About 5300 L - the number that drives fill times and chemical dosing.
Quick solve: practice it
A tank is 1.2 m in diameter and 2.5 m tall. What is its capacity?
Quick-solve habit: calculate, then ask yourself - does this answer make sense in real units?
Games that use this mathematics
Apply the calculation inside a workplace simulation.