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

The correct equation is (a) because π/1 = C2/r2, $C_2= 2\pi r$

How to determine the correct equation?

The complete question is added as an attachment

The given parameters are:

d1 = 1

d2 = 2r

The circumferences of the circles are calculated as:

C = πd

This gives

C1 = π * 1 = π

C2 = π * 2r = 2πr

So, we have:

C1 = π

C2 = 2πr

and

d1 = 1

d2 = 2r

Divide both equations

$\frac{C_2}{d_1} = \frac{C_2}{d_2}$

$\frac{\pi}{1} = \frac{2\pi r}{2r}$

This gives

$\frac{\pi}{1} = \frac{C_2}{2r}$

Hence, the correct equation is (a) because π/1 = C2/r2, $C_2= 2\pi r$

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