Cones and pyramids
What you'll learn
Understand the 1/3 that turns a cylinder into a cone — and why it's exactly a third.
A cone has the same circular base and height as a cylinder — but it tapers to a point. That taper costs it exactly two-thirds of the volume.
The one-third rule
A cone (or any pyramid) holds a third of the prism with the same base and height:
V = ⅓ × base area × height
For a cone that's ⅓ π r² h. With radius 2 and height 5: ⅓ × π × 4 × 5 ≈ 20.9 cubic units — exactly a third of the cylinder from the last lesson.
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Why a third?
Pour three identical cones of water into the matching cylinder and it fills right to the top — every time. The same 1/3 holds for any pyramid versus its prism. The point always costs you two-thirds of the space.
Check your understanding
Question 1 of 2
A cone and a cylinder share the same base and height. The cone's volume is what fraction of the cylinder's?