Calculate the volume in a. cubic cm b. cu. in c. L of a prism  ( where V = πr2h) that is 6 m long, 450 cm wide and 3000 mm high.

To calculate the volume of a prism using the formula \( V = \pi r^2 h \), we need to first determine if this formula is appropriate for the given prism dimensions. The given formula is for the volume of a cylindrical prism, not a rectangular prism. Since the dimensions provided are length, width, and height, the shape seems to be a rectangular prism.

For a rectangular prism, the volume is calculated by:

\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]

### Step 1: Convert all dimensions to consistent units (centimeters)

- Length: 6 meters = \(6 \times 100 = 600 \) cm
- Width: 450 cm (already in cm)
- Height: 3000 mm = \( \frac{3000}{10} = 300 \) cm

### Step 2: Calculate the Volume in Cubic Centimeters

\[
V = 600 \, \text{cm} \times 450 \, \text{cm} \times 300 \, \text{cm}
\]

Let's calculate this:

\[
V = 600 \times 450 \times 300
\]

### Step 3: Convert to Other Units

- **Cubic Inches:**  
1 cm\(^3\) = 0.0610237 in\(^3\)
  
- **Liters:**  
1 cm\(^3\) = 0.001 liters

Let's compute the volume and convert it to the desired units.The volume of the rectangular prism is:

a. **Cubic centimeters (cm\(^3\))**: \(81,000,000\) cm\(^3\)

b. **Cubic inches (in\(^3\))**: \(4,942,919.7\) in\(^3\)

c. **Liters (L)**: \(81,000\) L

Would you like more details, or do you have any questions?

### Related Questions:

1. How do you calculate the volume of a cylindrical prism?
2. What is the difference between cubic centimeters and liters?
3. How would you convert cubic inches back to cubic centimeters?
4. What are other units used for measuring volume, and how are they converted?
5. How do the formulas for volume differ for various geometric shapes?

**Tip:** Always ensure that all measurements are in the same units before performing calculations to avoid errors.

Calculate the volume in a. cubic cm b. cu. in c. L of a prism (where V = πr^2h) that is 6 m long, 450 cm wide, and 3000 mm high.

Learn how to calculate the volume of a rectangular prism that is 6 meters long, 450 cm wide, and 3000 mm high. Step-by-step solution includes converting between cubic centimeters, cubic inches, and liters. Suitable for middle school students (Grades 6-8).

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