If a circle has a diameter of 10 units, what is the circumference using C = πd?

If a circle has a diameter of 10 units, what is the circumference using C = πd?

• A. 10π
• B. 20
• C. 5π
• D. 2π

Answer: (A)

The key idea is that the circumference relates to the diameter through the constant π: C = πd. If the diameter is 10, you multiply by π to get C = π × 10 = 10π. That is the exact circumference (about 31.42 units if you approximate π). The same result would come from the radius form, since the radius is 5 and C = 2πr = 2π×5 = 10π. The other numbers would come from dropping π or misusing the radius/diameter relation, which isn’t consistent with the given formula.

The key idea is that the circumference relates to the diameter through the constant π: C = πd. If the diameter is 10, you multiply by π to get C = π × 10 = 10π. That is the exact circumference (about 31.42 units if you approximate π). The same result would come from the radius form, since the radius is 5 and C = 2πr = 2π×5 = 10π. The other numbers would come from dropping π or misusing the radius/diameter relation, which isn’t consistent with the given formula.