GMY-03

Sphere volume

Also 4πR².

Reading speed

Geometrysphere

Governing equation

V=4\\pi R^3/3

where

R: R (m)
V: V (m³)
A: A (m²)

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-03 — Sphere volume) is the form associated with sphere. Working symbols: $R$ $\rightarrow$ $V$ , $A$ . Also 4πR².

Purpose

Purpose: compute

V

A

from

R

in Geometry via

V=4\\pi R^3/3

Also 4πR². Use it when a real geometry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

R = 1.000\,\mathrm{m}

, the governing relation

V=4\\pi R^3/3

yields

V = 4.1888\,\mathrm{m^{3}}

A = 12.5664\,\mathrm{m^{2}}

. Also 4πR². Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

R R1 m

Outputs

V V4.1888 m³
A A12.5664 m²

Reading speed

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Narration of this film

Also 4πR².

Reading speed

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