Problem preview

G-GMD.1 Core M2-037-R01-V04

Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.

Connect the two circumference formulas

Problem

A circle has symbolic radius \(r\) and diameter \(d=2r\). Evaluate or transform \(\text{both}~\text{circumference}~\text{forms}\).

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Because d = 2r, πd = 2πr; the forms are not equivalent.

The forms are equivalent because d = r/2.

Because d = 2r, πd = π(2r) = 2πr; the two circumference forms are equivalent.

πd and πr² are the same circumference formula.

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Curriculum context

Course: Math II
Standard: G-GMD.1
Category: Geometry
Domain: Geometric Measurement and Dimension
Objective: Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Problem type: Connect the two circumference formulas