Question
what is the volume of a perfume bottle with a height of 12.4 cm and a radius of 6.2 cm
Answers
GPT-4o mini
To calculate the volume of a perfume bottle, we can assume that it has a cylindrical shape. The formula for the volume \( V \) of a cylinder is:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14159.
Given:
- Height \( h = 12.4 \, \text{cm} \)
- Radius \( r = 6.2 \, \text{cm} \)
Plugging in the values:
\[
V = \pi (6.2)^2 (12.4)
\]
Calculating \( (6.2)^2 \):
\[
(6.2)^2 = 38.44
\]
Now substituting back into the volume formula:
\[
V = \pi (38.44)(12.4) \approx 3.14159 \times 38.44 \times 12.4
\]
Now calculate \( 38.44 \times 12.4 \):
\[
38.44 \times 12.4 = 476.576
\]
Then multiply by \( \pi \):
\[
V \approx 3.14159 \times 476.576 \approx 1498.88 \, \text{cm}^3
\]
Therefore, the volume of the perfume bottle is approximately **1498.88 cm³**.
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14159.
Given:
- Height \( h = 12.4 \, \text{cm} \)
- Radius \( r = 6.2 \, \text{cm} \)
Plugging in the values:
\[
V = \pi (6.2)^2 (12.4)
\]
Calculating \( (6.2)^2 \):
\[
(6.2)^2 = 38.44
\]
Now substituting back into the volume formula:
\[
V = \pi (38.44)(12.4) \approx 3.14159 \times 38.44 \times 12.4
\]
Now calculate \( 38.44 \times 12.4 \):
\[
38.44 \times 12.4 = 476.576
\]
Then multiply by \( \pi \):
\[
V \approx 3.14159 \times 476.576 \approx 1498.88 \, \text{cm}^3
\]
Therefore, the volume of the perfume bottle is approximately **1498.88 cm³**.