https://file.aiquickdraw.com/mathbot/file/1729609524268seb4kpzg.jpg

To find the volume of a cylinder, we use the formula:

\[
V = \pi r^2 h
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height (or length) of the cylinder,
- \( \pi \) is approximately 3.14159.

From the image:
- Radius \( r = 3 \, \text{cm} \),
- Length \( h = 12 \, \text{cm} \).

Substituting these values into the formula:

\[
V = \pi (3^2)(12)
\]
\[
V = \pi (9)(12)
\]
\[
V = 108\pi
\]
\[
V \approx 108 \times 3.14159
\]
\[
V \approx 339.29 \, \text{cm}^3
\]

Rounding to the nearest integer:

\[
V \approx 339 \, \text{cm}^3
\]

The volume of the cylinder is approximately **339 cm³**.

Would you like further explanation or have any other questions?

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Here are some related questions:
1. How does the formula for the surface area of a cylinder compare to that of the volume?
2. What happens to the volume if you double the radius but keep the height the same?
3. How does the volume change if both the radius and the height are doubled?
4. Can you derive the formula for the volume of a cone, and how does it differ from that of a cylinder?
5. What are some real-world applications of calculating cylinder volumes?

**Tip:** Always check units in volume calculations, especially if the problem involves different unit systems!

The cylinder below has a radius of 3 cm and a length of 12 cm. Work out the volume of the cylinder. Give your answer to the nearest integer.

Learn how to calculate the volume of a cylinder with a radius of 3 cm and length of 12 cm. Step-by-step guide using the formula V = πr²h. Final volume is approximately 339 cm³. Suitable for Grades 6-8.

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