GMY-25

Circular sector

Sector area.

Reading speed

GoverningCircular sector

Governing equation

A=\\tfrac12 r^2\\theta

where

r: r (m)
th: th (rad)
A: Circular sector (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-25 — Circular sector) is the form associated with Circular sector. Working symbols: $r$ , $th$ $\rightarrow$ $A$ . Sector area. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

A

from

r

th

in Geometry via

A=\\tfrac12 r^2\\theta

Sector area. 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 = 2.000\,\mathrm{m}

th = 1.200\,\mathrm{rad}

, the governing relation

A=\\tfrac12 r^2\\theta

yields

A = 2.400\,\mathrm{m^{2}}

. 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

r r2 mth th1.2 rad

Outputs

Circular sector A2.400 m²

Reading speed

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Narration of this film

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

Sector area. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube