GMY-27

Pyramid volume

Any pyramid/cone.

Reading speed

GoverningPyramid volume

Governing equation

V=\\tfrac13 A h

where

A: A (m²)
h: h (m)
V: Pyramid volume (m³)

Lecture brief

Historical brief

Pythagoras, Heron, spherical trigonometry and the sphere’s volume are the measuring arts that predate calculus. The sheets compute length, area and angle on plane and sphere. This sheet (GMY-27 — Pyramid volume) is the form associated with Pyramid volume. Working symbols: $A$ , $h$ $\rightarrow$ $V$ . Any pyramid/cone. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

V

from

A

h

in Geometry via

V=\\tfrac13 A h

Any pyramid/cone. Use it when a real geometry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 12.000\,\mathrm{m^{2}}

h = 4.000\,\mathrm{m}

, the governing relation

V=\\tfrac13 A h

yields

V = 16.000\,\mathrm{m^{3}}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

A A12 m²h h4 m

Outputs

Pyramid volume V16.000 m³

Reading speed

Watch on YouTube

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Any pyramid/cone. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube