Volume of Cylinders
The volume of any three-dimensional shape equals the area of its base multiplied by its height. For cylinders, the formula is V = Bh, where B is the base area and h is the height. Since the base of a cylinder is a circle with area πr², the complete formula becomes V = πr²h.
Let's see how this works in practice. If you have a cylinder with radius 3 inches and height 10 inches, you calculate the volume by plugging these values into the formula: V = π(3²)(10) = 282.7 in³. The answer is always expressed in cubic units, showing it's a volume measurement.
Similarly, for a cylinder with radius 3.2 cm and height 13 cm, the volume is V = π(3.2²)(13) = 418.2 cm³. Notice how we square the radius first, then multiply by height and π.
Quick Tip: When calculating cylinder volume, remember to use the radius (half the diameter) in your formula, not the diameter itself. Many mistakes happen when students use the wrong measurement!