Learning goals
- Double the radius and the area becomes 4× larger — not 2× larger.
- At r = 4, the readout shows ≈ 50.27 — exactly π × 16.
- Area is a 2D measure, which is why its units carry a square (cm², m²).
Drag the Radius, Feel r²
See area grow quadratically
Drag the radius and watch the circle area update live. When the radius grows by 1, the area grows by a new square layer, not by a straight line.
What this game shows · r² Grows Quadratically
When you double the radius of a circle, the area does not double — it quadruples. The radius slider exposes this quadratic growth: drag from r = 1 to r = 5 and watch the area grow as 1, 4, 9, 16, 25 (times π).
- Linear
- circumference grows as 2πr — double r, double C.
- Quadratic
- area grows as πr² — double r, quadruple A.
- Square units
- area is 2-D, hence cm², m², etc.
Aligned with CCSS 7.G.B.4 (informal derivation of area and circumference of a circle).
Radius slider
Area grows with the square of the radius, not with the radius itself.
A ≈ 50.27
Geometry and measurement model
Who this demo helps, and where to practice next
Drag the Radius, Feel r² is built for students who memorize formulas before seeing the shape decomposition. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Drag the Radius, Feel r² helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
How to play
- 1 Identify the shape pieces before calculating.
- 2 Drag or replay the model until the formula can be described from the picture.
- 3 Open the related geometry topic when the student can explain area, perimeter, or surface area in units.
Continue with guided practice
FAQ
Tap to expand Radius and area, r squared.
01 Why does doubling r quadruple the area? 4× area
Area = πr². If r → 2r, area becomes π(2r)² = 4πr² — exactly four times bigger.
02 How does the gold r × r square in the corner help? r² as a square
It's the literal r² seen as a square. Each unit growth in r adds a new "ring" of unit squares — the visible meaning of r².
03 Why does circumference grow only linearly? C linear, A quadratic
Because C = 2πr is linear in r. Doubling r doubles C, not quadruples it. Area and circumference scale at different rates.
04 Which grade is this game for? Grades 6–7
Grades 6–7, aligned with CCSS 7.G.B.4. Excellent first encounter with quadratic growth.