https://file.aiquickdraw.com/mathbot/file/1728650653528xpyyexss.jpg

The figure is a cylinder, and we need to find its volume. The formula for the volume of a cylinder is:

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

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

From the image:
- The radius \( r \) is \( 12 \) cm (as given for the diameter, so \( r = \frac{12}{2} = 6 \) cm).
- The height \( h \) is \( 12 \) cm.

### Step 1: Substitute the values into the formula:
\[
V = \pi (6 \text{ cm})^2 (12 \text{ cm})
\]

\[
V = \pi \times 36 \text{ cm}^2 \times 12 \text{ cm}
\]

\[
V = \pi \times 432 \text{ cm}^3
\]

\[
V = 432\pi \text{ cm}^3
\]

This is the exact volume in terms of \( \pi \).

### Step 2: Approximate the volume using \( \pi \approx 3.14159 \):
\[
V \approx 432 \times 3.14159 \text{ cm}^3
\]

\[
V \approx 1357.17 \text{ cm}^3
\]

### Final Answers:
- **Exact Volume**: \( 432\pi \text{ cm}^3 \)
- **Approximate Volume**: \( 1357.17 \text{ cm}^3 \)

Would you like any further details or have any questions?

### Related Questions:
1. What is the surface area of the same cylinder?
2. How would the volume change if the height were doubled while keeping the radius the same?
3. What is the volume of a cylinder if the diameter is reduced to 8 cm but the height remains at 12 cm?
4. If the volume of a cylinder is known, how can you find its height?
5. How does changing the radius affect the volume of a cylinder proportionally?

**Tip:** Remember, the volume of a cylinder is directly proportional to the square of its radius, so small changes in the radius lead to significant changes in the volume.

Find the volume of a cylinder with a radius of 6 cm and a height of 12 cm. Give both the exact value in terms of π and an approximation to the nearest hundredth of a unit.

Learn how to calculate the volume of a cylinder with a radius of 6 cm and a height of 12 cm. This problem demonstrates how to use the cylinder volume formula and provides both an exact solution in terms of π and an approximation to the nearest hundredth. Suitable for students in Grades 8-10.

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