Area of Circles

Geometry · Axiom Academy

Measuring round shapes with the magic of pi — the distance around, the space inside, and the one constant that ties them together. Take any circle and divide its circumference (the distance once around) by its diameter (the distance straight across). You always get the same number — about 3.14159… — no matter how big or small the circle is. That number is . is the ratio of circumference to diameter so the circumference is diameters long Two formulas do all the work. One measures the distance around the circle; the other measures the space inside it. Both are built from the radius and . space inside · square the radius! The area picture is the surprising one: slice the disk into thin wedges and rearrange them, and they fit into a rectangle that is r tall and r wide — area . 3. What Happens If You Double the Radius? Because area depends on r^2 but circumference depends on r , scaling the radius does not scale them the same way. Watch the radius grow from r to 2r and compare the two gauges. 4. Worked Example: Area from a Diameter The hardest version of the area problem hands you the diameter , not the radius. Watch the whole computation build: a circle of diameter 12 in is measured, the diameter is halved to a radius, the radius is squared , and that is scaled by to give the area. Press play. The same substitute and simplify recipe handles every circle question. Here are three more, worked the same way ( ): Find the circumference of a circle with radius 7 cm.

This is the written version of the interactive lesson above. See the full Geometry course.