https://file.aiquickdraw.com/mathbot/file/17271939341548jv4esv5.jpg

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

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

Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height (or length) of the cylinder.
- \( \pi \) is a constant, approximately equal to 3.1416.

From the image:
- The diameter of the cylinder is 12 cm, so the radius \( r \) is half of that: \( r = \frac{12}{2} = 6 \) cm.
- The height (length) \( h \) is 40 cm.

Now, let's plug these values into the formula:

\[
V = \pi (6^2) \times 40 = \pi \times 36 \times 40 = 1440\pi
\]

Now, calculating the volume:

\[
V \approx 1440 \times 3.1416
\]

I'll compute the result.The volume of the cylinder is approximately **4523.9 cm³**, rounded to one decimal place.

Do you need more details or have any questions? Here are five related questions for further exploration:

1. How would the volume change if the radius were doubled?
2. What is the surface area of the cylinder in this case?
3. How does the volume of a cylinder compare to that of a cone with the same base and height?
4. How would the volume change if the height of the cylinder were reduced by half?
5. What is the volume of a cylinder with a height of 50 cm and a radius of 5 cm?

**Tip**: The volume of any 3D shape is directly proportional to its dimensions, meaning a small change in radius or height can significantly impact the volume.

Work out the volume of the cylinder below. If your answer is a decimal, give it to 1 d.p. (The cylinder has a diameter of 12 cm and a height of 40 cm.)

Learn how to calculate the volume of a cylinder with a diameter of 12 cm and a height of 40 cm using the formula V = πr^2h. This solution includes a detailed step-by-step guide, suitable for students in Grades 7-9.

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