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PEAZIT Aha card

A pyramid has one third of the matching prism's volume

A pyramid narrows toward its apex. Its volume is one third of a prism with the same base and height.

Square base with side 6 cm; perpendicular height 5 cm.

Relation	Meaning
V = B × h / 3	Divide prism volume B × h by three.
B = 6 × 6 = 36 cm²	First calculate the base area.
V = 36 × 5 / 3 = 60 cm³	36 × 5 / 3 = 60.

One worked example

V = B × h / 3Divide prism volume B × h by three.
B = 6 × 6 = 36 cm²First calculate the base area.
V = 36 × 5 / 3 = 60 cm³36 × 5 / 3 = 60.

Watch out: Height is the perpendicular distance from apex to base plane, not a sloping edge or face height.

Goal, prerequisites and card origin

What you will learn: Find volume from base area and perpendicular height.

What you need first: Base area and prism volume.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

A pyramid narrows toward its apex. Its volume is one third of a prism with the same base and height.

Without JavaScript, write your answer elsewhere before opening the solution.A square base has side 4 cm and perpendicular height is 6 cm. Find volume in cm³. Enter a number.

Solution — open after your own attempt

32 4² × 6 / 3 = 32 cm³.

A question for your next return: Base area is 30 cm² and perpendicular height 5 cm. What is the volume in cm³?

Solution — open after your own attempt

50 30 × 5 / 3 = 50 cm³.

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