Question
A cylinder has a height of 18 millimeters and a diameter of 18 millimeters. What is its volume? Use 𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
Answers
GPT-4o mini
To find the volume of a cylinder, you can use the formula:
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given that the diameter is 18 millimeters, the radius \( r \) is half of the diameter:
\[
r = \frac{d}{2} = \frac{18 \, \text{mm}}{2} = 9 \, \text{mm}
\]
The height \( h \) is given as 18 millimeters. Now, substituting the values into the volume formula:
\[
V = \pi (9 \, \text{mm})^2 (18 \, \text{mm})
\]
\[
V = \pi \times 81 \, \text{mm}^2 \times 18 \, \text{mm}
\]
\[
V = \pi \times 1458 \, \text{mm}^3
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 3.14 \times 1458 \, \text{mm}^3
\]
\[
V \approx 4577.32 \, \text{mm}^3
\]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[
\boxed{4577.32} \, \text{mm}^3
\]
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given that the diameter is 18 millimeters, the radius \( r \) is half of the diameter:
\[
r = \frac{d}{2} = \frac{18 \, \text{mm}}{2} = 9 \, \text{mm}
\]
The height \( h \) is given as 18 millimeters. Now, substituting the values into the volume formula:
\[
V = \pi (9 \, \text{mm})^2 (18 \, \text{mm})
\]
\[
V = \pi \times 81 \, \text{mm}^2 \times 18 \, \text{mm}
\]
\[
V = \pi \times 1458 \, \text{mm}^3
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 3.14 \times 1458 \, \text{mm}^3
\]
\[
V \approx 4577.32 \, \text{mm}^3
\]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[
\boxed{4577.32} \, \text{mm}^3
\]