calculate the volume of a cylinder prism that has the base and top diameter of 66mm and height of 8.5cm work out in cm

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

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

Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height

Given:
- Diameter of the base (and top) = 66 mm
- Height = 8.5 cm

First, we need to convert the diameter to the radius and ensure all measurements are in the same units. The diameter is given in millimeters, so we convert it to centimeters.

\[ \text{Diameter} = 66 \text{ mm} = 6.6 \text{ cm} \]
\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{6.6 \text{ cm}}{2} = 3.3 \text{ cm} \]

Now, we can plug the values into the formula:

\[ V = \pi (3.3 \text{ cm})^2 (8.5 \text{ cm}) \]

Calculating step-by-step:

1. Calculate the radius squared:
\[ 3.3 \text{ cm} \times 3.3 \text{ cm} = 10.89 \text{ cm}^2 \]

2. Multiply by the height:
\[ 10.89 \text{ cm}^2 \times 8.5 \text{ cm} = 92.565 \text{ cm}^3 \]

3. Multiply by \(\pi\) (using \(\pi \approx 3.14159\)):
\[ 92.565 \text{ cm}^3 \times 3.14159 \approx 290.86 \text{ cm}^3 \]

Therefore, the volume of the cylinder is approximately \(290.86 \text{ cm}^3\).

Would you like more details or have any questions? 

Here are five more questions you might consider asking:
1. How do you convert between different units of measurement in geometry problems?
2. Can you show how to find the surface area of the same cylinder?
3. What is the significance of \(\pi\) in calculating the volume of a cylinder?
4. How would the volume calculation change if the height were given in meters?
5. Can you explain the relationship between diameter, radius, and circumference of a circle?

**Tip:** When dealing with geometry problems, always ensure that all measurements are in the same unit before performing calculations to avoid errors.

Learn how to calculate the volume of a cylinder prism with a diameter of 66mm and a height of 8.5cm using the volume formula. This problem involves converting units, applying the cylinder volume formula, and understanding geometric calculations. Suitable for Grades 7-9.

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