Question

Two circles are shown in the diagram.

Circles C 1 and C 2 are shown. The diameter of circle 1 is 1. The diameter of circle 2 is 2 r.

Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d1 = 1, C1 = π, and d2 = 2r into the proportion.

StartFraction C 1 Over d 1 EndFraction = StartFraction C 2 Over d 2 EndFraction

Which shows how to correctly solve for C2, the circumference of any circle with radius r?

Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = 2 r pi
Because StartFraction 1 Over pi EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = StartFraction 2 r Over pi EndFraction
Because StartFraction pi Over 2 r EndFraction = StartFraction C 2 Over 1 EndFraction , C 2 = StartFraction pi Over 2 r EndFraction
Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 4 r EndFraction , C 2 = 4 r pi

Answer 1

Use C1/d1 = C2/d2. With C1 = π and d1 = 1 and d2 = 2r:

π/1 = C2/(2r) ⇒ C2 = π·(2r) = 2πr.

So the first choice is correct.