To find the volume of a perfume bottle that is shaped like a sphere, we first need to calculate the radius using the given circumference.
The formula for the circumference \( C \) of a sphere (or a circle) is:
\[ C = 2 \pi r \]
We are given that the circumference is 6.2 cm. We can set up the equation:
\[ 6.2 = 2 \pi r \]
Replacing \(\pi\) with 3.14, we have:
\[ 6.2 = 2 \times 3.14 \times r \]
Now, simplify the right side:
\[ 6.2 = 6.28r \]
Next, solve for \( r \):
\[ r = \frac{6.2}{6.28} \approx 0.987 , \text{cm} \]
Next, we can use this radius to find the volume \( V \) using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Substituting \(\pi \) with 3.14 and \( r \) with approximately 0.987 cm:
\[ V = \frac{4}{3} \times 3.14 \times (0.987)^3 \]
First, calculate \( (0.987)^3 \):
\[ (0.987)^3 \approx 0.962 \]
Now we substitute this value into the volume formula:
\[ V \approx \frac{4}{3} \times 3.14 \times 0.962 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.1867 \]
Now multiply this by \( 0.962 \):
\[ V \approx 4.1867 \times 0.962 \approx 4.028 \]
Thus, the volume of the perfume bottle is approximately:
\[ \boxed{4.03} , \text{cm}^3 \]