Geometry
Volume of Cylinders – V = πr²h
A cylinder is really just a “circular prism,” so its volume follows the exact same cross-section-times-length logic: V = πr²h, where πr² is the area of the circular cross-section and h is the height. This is one more example of the general prism volume rule you just learned, applied to a circular cross-section instead of a polygon.
Because the formula depends on r² but only on h to the first power, a cylinder's volume is far more sensitive to changes in radius than to changes in height – doubling the radius quadruples the volume, while doubling the height only doubles it.
Calculating a Cylinder's Volume
V = πr²h. Volume scales with r², so scaling the radius by a factor of k scales the volume by k².
Find the volume of a cylinder with radius 4 cm and height 9 cm.
V = π(4)²(9) = π(16)(9) = 144π ≈ 452.39 cm³.
Real-Life Application
- Drink cans: calculating how much liquid a cylindrical can holds.
- Water tanks: finding the capacity of a cylindrical storage tank.
- Pipes: calculating how much water flows through a cylindrical pipe.
Key Takeaways
- A cylinder's volume formula is V = πr²h.
- A cylinder is a “circular prism,” following the same cross-section × length rule.
- Volume is more sensitive to radius changes than height changes, since it depends on r².
Practice: Volume of Cylinders
Volume of Cylinders