Find Both Radius and Area From Circumference

Start with the circumference and area sheets, then use the missing diameter and radius sheets for practice with division. Use the area derivation sheet to answer why the formula works.

Find the radius from a circumference such as 31.4 cm, then use it to find the area of the circle. The directions on the page read: C is the circumference. Use C = 2πr to find the radius r, then A = πr² to find the area A. Use 3.14 for π. Show your work in the box and include units. An answer key is included.

Yes, both. We made it for 7th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

The circumference is C = πd, or C = 2πr, where d is the diameter and r is the radius. For r = 7 cm and 3.14 for π, C ≈ 43.96 cm. Circumference From Radius or Diameter has students write the numbers in the formula first.

The area is A = πr², so square the radius and multiply by π. If a diameter is given, halve it to find the radius first. Area of Circles From Labeled Diagrams practices this and asks for square units.

Divide the circumference by π to get the diameter, or by 2π to get the radius. For C = 14π cm, the diameter is 14 cm. Missing Diameter From Whole-Number Circumferences and Missing Radius From Decimal Circumferences are two of the sheets.

Cut a circle into equal wedges and lay them side by side to make a near rectangle. Its height is r and its base is half the circumference, πr, so its area is πr × r. Why Circle Area Is Pi Times Radius Squared walks through this.