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PEAZIT Aha card

Circle area grows with the square of its radius

Rearranging many narrow sectors approaches a rectangle with sides πr and r. Its area is πr².

A 3 cm radius gives approximately 28.26 cm².

Relation	Meaning
S = πr²	We need the radius, not the diameter.
r = 3; r² = 9	Square the radius.
S ≈ 3.14 × 9 = 28.26 cm²	Multiply the squared radius by π.

One worked example

S = πr²We need the radius, not the diameter.
r = 3; r² = 9Square the radius.
S ≈ 3.14 × 9 = 28.26 cm²Multiply the squared radius by π.

Watch out: Doubling the radius quadruples area. Halve a given diameter before substituting.

Goal, prerequisites and card origin

What you will learn: Calculate the area inside a circle.

What you need first: Radius, squaring a number and area.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

Rearranging many narrow sectors approaches a rectangle with sides πr and r. Its area is πr².

Without JavaScript, write your answer elsewhere before opening the solution.A circle has radius 4 cm. Using π = 3.14, find the area in cm². Enter a number.

Solution — open after your own attempt

50.24 3.14 × 4² = 3.14 × 16 = 50.24 cm².

A question for your next return: The diameter is 10 cm. Using π = 3.14, find the area in cm². Enter a number.

Solution — open after your own attempt

78.5 The radius is 5 cm; 3.14 × 25 = 78.5 cm².

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