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Circle Area and Circumference Calculator

Run the Circle Area and Circumference Calculator MicroSim Fullscreen
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About This MicroSim

A circle is drawn with its radius (red) and diameter (dashed green). As the radius changes, the panels on the right substitute the current value into the two circle formulas:

  • Circumference: \(C = 2\pi r\)
  • Area: \(A = \pi r^2\)

The third panel answers a question that students often get wrong: what happens when the radius doubles? The circumference doubles, because \(r\) appears to the first power. The area becomes four times as large, because \(r\) is squared.

How to Use

  1. Drag the Radius slider from 2 cm to 20 cm and watch the circle and both calculations change.
  2. Use the r = 5, r = 10, and r = 15 buttons to jump to common values and compare the results.
  3. Read the If the radius doubles panel and check its numbers by moving the slider to twice the current radius.

Iframe Embed Code

<iframe src="main.html"
        height="502"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

9-12 (High School Geometry)

Duration

10-15 minutes

Prerequisites

Radius and diameter of a circle, the meaning of π, and squaring a number.

Bloom's Taxonomy Level

Apply (L3)

Learning Objective

Students will be able to calculate the circumference and area of a circle from its radius and analyze how a change in radius affects each measurement.

Activities

  1. Predict (3 min): Before touching the slider, students predict the circumference and area for r = 5 and r = 10, then check with the preset buttons.
  2. Calculate (5 min): Students choose three radii, compute C and A by hand, and compare with the Measurements panel.
  3. Analyze (5 min): Students record C and A for r = 4, 8, and 16 in a table and describe the pattern in each column.

Assessment

Students find the circumference and area of a circle with a radius the MicroSim cannot show (for example r = 25 cm) and explain, without recalculating, how the area compares with the area at r = 12.5 cm.

References

  1. Wikipedia. Area of a circle.
  2. Wikipedia. Circumference.
  3. Common Core State Standards Initiative. High School Geometry: Geometric Measurement and Dimension (HSG-GMD.A.1).