Volume of Pyramids and Cones

Pyramid volume uses the formula V = ⅓Ah, where A is the base area and h is the height. Think of it as taking one-third of what a rectangular prism would be with the same base and height.

For cone volume, you'll use V = ⅓πr²h, where r is the radius and h is the height. Notice how both formulas start with that crucial "one-third" - that's because pyramids and cones taper to a point, making them exactly one-third the volume of their corresponding prisms or cylinders.

Let's look at a practical example: if you've got a pyramid with a base area of 100m² and height of 12m, simply plug into the formula: V = ⅓ × 100 × 12 = 400m³. For a cone with radius 15cm and height 10cm: V = ⅓ × π × 15² × 10 = 2,356.19cm³.

Top Tip: Always remember that pyramids and cones are exactly one-third the volume of prisms and cylinders with the same base and height - this helps you check if your answer seems reasonable!

The key to success with these problems is identifying which formula to use (pyramid or cone), calculating the base area correctly, and remembering that fraction of one-third. With practice, you'll be solving these volume problems with confidence.