Circumference from Diameter
The circumference of a circle is found by multiplying its diameter by π (≈ 3.14). In Grade 6 Saxon Math Course 1, students use the formula C = π × d. For a circle with diameter 14 cm: C = 3.14 × 14 = 43.96 cm. If the radius is given instead, first double it to get the diameter: d = 2r, then apply C = πd. This formula is derived from the observation that a circle's circumference is always approximately 3.14 times its diameter, regardless of size.
Key Concepts
Property To find the circumference of a circle, multiply the diameter of the circle by $\pi$. The formula is $C = \pi d$.
Examples A bicycle tire with a 20 inch diameter has a circumference of $C \approx 3.14 \cdot 20 \text{ in.} = 62.8 \text{ in.}$ A penny with a 0.75 inch diameter has a circumference of $C \approx 3.14 \cdot 0.75 \text{ in.} \approx 2.36 \text{ in.}$ A plate with a diameter of 10 inches has a circumference of $C \approx 3.14 \cdot 10 \text{ in.} = 31.4 \text{ in.}$.
Explanation If you know the distance straight across a circle, you've got a golden ticket! This distance is the diameter, and all you have to do is multiply it by our good friend $\pi$ (about 3.14) to find the circumference. It’s a simple one step trick to calculate the full distance around a pizza, a coin, or a wheel.
Common Questions
What is the formula for circumference using diameter?
C = π × d ≈ 3.14 × d.
Find the circumference of a circle with diameter 14 cm.
C = 3.14 × 14 = 43.96 cm.
Find the circumference if the radius is 7 cm.
d = 2 × 7 = 14 cm. C = 3.14 × 14 = 43.96 cm.
What is the circumference formula using radius?
C = 2πr, since d = 2r. So C = 2 × 3.14 × r.
Why is π approximately 3.14?
π is the ratio of any circle's circumference to its diameter. This ratio is constant for all circles and equals approximately 3.14159…