Question

The circle-shaped part of the necklace above has a diameter of 5 mm.

The circumference of the circle-shaped part of each of the earrings is one-half the circumference of the necklace.

What is the circumference of the circle-shaped part of one of the earrings? (Use 3.14 for .)
A.
15.7 mm
B.
3.925 mm
C.
31.4 mm
D.
7.85 mm

Answer 1

To find the circumference of the circle-shaped part of the necklace, we use the formula for the circumference of a circle:

\[
C = \pi d
\]

where \(d\) is the diameter.

Given that the diameter of the necklace is 5 mm, we can calculate the circumference as follows:

\[
C_{\text{necklace}} = 3.14 \times 5 = 15.7 \text{ mm}
\]

The problem states that the circumference of the circle-shaped part of each of the earrings is one-half the circumference of the necklace. Therefore, we need to calculate one-half of the circumference of the necklace:

\[
C_{\text{earring}} = \frac{1}{2} C_{\text{necklace}} = \frac{1}{2} \times 15.7 = 7.85 \text{ mm}
\]

Thus, the circumference of the circle-shaped part of one of the earrings is:

\[
\boxed{7.85 \text{ mm}}
\]

So the correct option is **D. 7.85 mm**.