To find the volume of the perfume bottle, we can use the formula for the volume of a cylinder:
\[ V = \pi \times r^2 \times h \]
where:
- \( \pi \) is approximately 3.14,
- \( r \) is the radius,
- \( h \) is the height.
From the dimensions given:
- The height \( h \) of the bottle is 12.4 cm.
- The width (side to side) measures 6.2 cm. Since this dimension is the diameter of the circular base, we can find the radius \( r \) by dividing the diameter by 2:
\[ r = \frac{6.2}{2} = 3.1 , \text{cm} \]
Now we can substitute the values into the volume formula:
\[ V = 3.14 \times (3.1)^2 \times 12.4 \]
First, calculate \( (3.1)^2 \):
\[ (3.1)^2 = 9.61 \]
Now, substitute that back into the volume formula:
\[ V = 3.14 \times 9.61 \times 12.4 \]
Now, calculate \( 3.14 \times 9.61 \):
\[ 3.14 \times 9.61 \approx 30.1584 \]
Now multiply this by the height \( h \):
\[ V \approx 30.1584 \times 12.4 \]
Calculating that gives:
\[ V \approx 373.96208 , \text{cm}^3 \]
Rounding to two decimal places, the volume of the perfume bottle is approximately:
\[ V \approx 373.96 , \text{cm}^3 \]