Circles
Lessons in this chapter
About Circles
Circles introduces the vocabulary and two core formulas: circumference and area, that describe a circle numerically, then applies area to shapes that combine a circle with other figures.
Identify parts of a circle names the radius (center to edge), diameter (edge to edge through the center, always twice the radius), and circumference (the distance around): the vocabulary every later circle formula depends on.
Solve problems on circumference of a circle introduces the formula C = πd (or C = 2πr), using π as the constant ratio between a circle’s circumference and its diameter to calculate the distance around a circle from its radius or diameter, and vice versa.
Find the area of a circle and composite figures introduces the area formula A = πr², then extends it to composite figures: shapes made of a circle (or part of one) combined with rectangles, triangles, or other polygons, where the total area is found by adding or subtracting the area of each individual piece.
The three lessons, Identify Parts of a Circle, Solve Problems on Circumference of a Circle and Find the Area of a Circle and Composite Figures, are 7th grade math worksheets your child works through in the page. Each question is marked as it is answered, which is the quickest way to catch the common slip of using the diameter where the formula asks for the radius. All three are free to try, with no login needed for your first 3.
Frequently asked questions
Identify Parts of a Circle names the radius, diameter, chord, center and circumference first, so the formulas that follow have something to refer to. Solve Problems on Circumference of a Circle introduces C = 2πr and the link between circumference and diameter, and Find the Area of a Circle and Composite Figures adds A = πr² and applies it to shapes built from circles and rectangles. This sits in the Common Core domain Geometry (7.G).
The radius is the distance from the center of a circle to its edge; the diameter is the distance across the circle through the center, and is always exactly twice the radius; the circumference is the total distance around the outside of the circle, the circle’s equivalent of a perimeter. Identify Parts of a Circle establishes all three before any formula uses them.
π (pi) is the constant ratio between any circle’s circumference and its diameter, no matter how big or small the circle, dividing its circumference by its diameter always gives the same number, approximately 3.14159. That constant relationship is exactly what makes the circumference and area formulas work for every circle.
Use C = πd if you know the diameter, or C = 2πr if you know the radius: both give the same answer, since diameter is always twice the radius. Solve Problems on Circumference of a Circle has kids practice both versions and also work backward, finding the radius or diameter from a known circumference.
Use A = πr², squaring the radius (not the diameter) and multiplying by π. Find the Area of a Circle and Composite Figures is where this formula gets introduced: a common early mistake is squaring the diameter instead, so it’s worth double-checking which measurement was given before plugging into the formula.
Using the diameter in a formula that calls for the radius, or vice versa, since the area formula A = πr² specifically needs the radius, a child given a diameter has to divide it by 2 first, which is easy to skip under time pressure.