Volume Worksheets - Free Printable

To solve the problem of finding the exact volume of each prism, we need to use the appropriate volume formulas for each shape. Let's go through each problem step by step.

Volume Formulas:

1. Rectangular Prism: \( V = \text{length} \times \text{width} \times \text{height} \)
2. Cylinder: \( V = \pi r^2 h \)
3. Triangular Prism: \( V = \frac{1}{2} \times \text{base} \times \text{height of triangle} \times \text{length of prism} \)
4. Cube: \( V = s^3 \) (where \( s \) is the side length)
5. Other Prisms: Use the area of the base times the height.

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Solutions:

#### 1) Rectangular Prism
- Dimensions: \( 12 \, \text{m} \times 4 \, \text{m} \times 9 \, \text{m} \)
- Volume: \( V = 12 \times 4 \times 9 = 432 \, \text{m}^3 \)

#### 2) Cylinder
- Radius: \( 8 \, \text{cm} \)
- Height: \( 14 \, \text{cm} \)
- Volume: \( V = \pi r^2 h = \pi (8)^2 (14) = \pi \cdot 64 \cdot 14 = 896\pi \, \text{cm}^3 \)

#### 3) Triangular Prism
- Base of triangle: \( 10 \, \text{mm} \)
- Height of triangle: \( 13 \, \text{mm} \)
- Length of prism: \( 10 \, \text{mm} \)
- Volume: \( V = \frac{1}{2} \times \text{base} \times \text{height of triangle} \times \text{length} \)
\[
V = \frac{1}{2} \times 10 \times 13 \times 10 = 650 \, \text{mm}^3
\]

#### 4) Triangular Prism
- Base of triangle: \( 15 \, \text{cm} \)
- Height of triangle: \( 11 \, \text{cm} \)
- Length of prism: \( 12 \, \text{cm} \)
- Volume: \( V = \frac{1}{2} \times \text{base} \times \text{height of triangle} \times \text{length} \)
\[
V = \frac{1}{2} \times 15 \times 11 \times 12 = 990 \, \text{cm}^3
\]

#### 5) Cube
- Side length: \( 7 \, \text{in} \)
- Volume: \( V = s^3 = 7^3 = 343 \, \text{in}^3 \)

#### 6) Rectangular Prism
- Dimensions: \( 5 \, \text{ft} \times 5 \, \text{ft} \times 10 \, \text{ft} \)
- Volume: \( V = 5 \times 5 \times 10 = 250 \, \text{ft}^3 \)

#### 7) Rectangular Prism
- Dimensions: \( 8 \, \text{ft} \times 8 \, \text{ft} \times 11 \, \text{ft} \)
- Volume: \( V = 8 \times 8 \times 11 = 704 \, \text{ft}^3 \)

#### 8) Trapezoidal Prism
- Bases of trapezoid: \( 9 \, \text{m} \) and \( 4 \, \text{m} \)
- Height of trapezoid: \( 6 \, \text{m} \)
- Length of prism: \( 15 \, \text{m} \)
- Area of trapezoid: \( A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} \)
\[
A = \frac{1}{2} \times (9 + 4) \times 6 = \frac{1}{2} \times 13 \times 6 = 39 \, \text{m}^2
\]
- Volume: \( V = \text{Area of base} \times \text{length} = 39 \times 15 = 585 \, \text{m}^3 \)

#### 9) Cylinder
- Radius: \( 3.6 \, \text{m} \)
- Height: \( 9 \, \text{m} \)
- Volume: \( V = \pi r^2 h = \pi (3.6)^2 (9) = \pi \cdot 12.96 \cdot 9 = 116.64\pi \, \text{m}^3 \)

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Final Answers:

1. \( 432 \, \text{m}^3 \)
2. \( 896\pi \, \text{cm}^3 \)
3. \( 650 \, \text{mm}^3 \)
4. \( 990 \, \text{cm}^3 \)
5. \( 343 \, \text{in}^3 \)
6. \( 250 \, \text{ft}^3 \)
7. \( 704 \, \text{ft}^3 \)
8. \( 585 \, \text{m}^3 \)
9. \( 116.64\pi \, \text{m}^3 \)

\[
\boxed{
\begin{array}{ll}
1. & 432 \, \text{m}^3 \\
2. & 896\pi \, \text{cm}^3 \\
3. & 650 \, \text{mm}^3 \\
4. & 990 \, \text{cm}^3 \\
5. & 343 \, \text{in}^3 \\
6. & 250 \, \text{ft}^3 \\
7. & 704 \, \text{ft}^3 \\
8. & 585 \, \text{m}^3 \\
9. & 116.64\pi \, \text{m}^3 \\
\end{array}
}
\]