Back to Explain circle area and volume formulas — Problem 1 · Task Set 33

Exercises: Informal Arguments for Volume and Area Formulas

Grade 10·24 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-gmd-a-1

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Fluency Practice

$A regular hexagon inscribed in a circle of radius 1, with one side labeled 1$

A regular hexagon is inscribed in a circle of radius 1. Each side of the hexagon equals the radius, so each side has length 1. What is the perimeter of the hexagon, and how does it compare to the circumference $2\pi \approx 6.28$ ?

Perimeter = 6; less than $2\pi$ , confirming the polygon approximates but underestimates the circumference

Perimeter = 6; equal to $2\pi$ , confirming the formula is exact

Perimeter = $6\pi$ ; greater than $2\pi$ , so the polygon overestimates the circumference

Perimeter = $3.14 \times 6$ ; because $\pi = 3.14$ , the perimeter is about 18.85