Find the volume of this perfume bottle: Hinit: V = 4/3 pi x r^3 (Use 3.14 for pi).

* it is 6.2 cm around the sphere

1 answer

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:

\[ \boxed{4.03} , \text{cm}^3 \]