Circle Formulas: Diameter and Circumference
Circle Formulas: Diameter and Circumference is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 13: Circles and Area. Students learn the fundamental formulas D = 2r and C = pi times D (or C = 2 pi r) to calculate the diameter and circumference of any circle. These formulas allow students to find the circumference given either the radius or diameter.
Key Concepts
The diameter of a circle is twice its radius. $$ D = 2 \times r $$ Circumference of a circle $$ C = \pi \times D \quad \text{or} \quad C = 2 \times \pi \times r $$.
Common Questions
What is the formula for circumference of a circle?
The circumference C equals pi times the diameter (C = pi x D) or equivalently C = 2 x pi x r, where r is the radius. For example, a circle with radius 5 cm has circumference C = 2pi(5) = 10pi, approximately 31.42 cm.
What is the relationship between diameter and radius?
The diameter equals twice the radius: D = 2r. Conversely, the radius equals half the diameter: r = D/2.
How do you find the circumference if you know the diameter?
Multiply the diameter by pi: C = pi x D. For example, a circle with diameter 8 inches has circumference C = 8pi, approximately 25.13 inches.
How do you find the diameter if you know the circumference?
Divide the circumference by pi: D = C divided by pi. For example, if the circumference is 30 inches, then D = 30/pi, approximately 9.55 inches.