Volumes of 3D-Shapes worksheet - Free Printable

Problem: Calculate the volumes of the given 3D shapes.

#### Step 1: Volume of Cubes
The formula for the volume of a cube is:
\[
V = e^3
\]
where \( e \) is the length of an edge of the cube.

##### Cube 1:
- Edge length (\( e \)) = 4 m
\[
V = 4^3 = 4 \times 4 \times 4 = 64 \, \text{m}^3
\]

##### Cube 2:
- Edge length (\( e \)) = 6.5 cm
\[
V = 6.5^3 = 6.5 \times 6.5 \times 6.5 = 274.625 \, \text{cm}^3
\]

#### Step 2: Volume of Prisms
The formula for the volume of a prism is:
\[
V = l \cdot w \cdot h
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

##### Prism 1:
- Length (\( l \)) = 5 dm
- Width (\( w \)) = 3 dm
- Height (\( h \)) = 7 dm
\[
V = 5 \times 3 \times 7 = 105 \, \text{dm}^3
\]

##### Prism 2:
- Length (\( l \)) = 8 hm
- Width (\( w \)) = 1.5 hm
- Height (\( h \)) = 2 hm
\[
V = 8 \times 1.5 \times 2 = 24 \, \text{hm}^3
\]

Final Answers:

1. Volume of Cube 1: \( \boxed{64 \, \text{m}^3} \)
2. Volume of Cube 2: \( \boxed{274.625 \, \text{cm}^3} \)
3. Volume of Prism 1: \( \boxed{105 \, \text{dm}^3} \)
4. Volume of Prism 2: \( \boxed{24 \, \text{hm}^3} \)

Explanation:

- For cubes, we use the formula \( V = e^3 \), where \( e \) is the edge length.
- For prisms, we use the formula \( V = l \cdot w \cdot h \), where \( l \), \( w \), and \( h \) are the length, width, and height, respectively.
- Each calculation involves straightforward multiplication based on the given dimensions. The units are preserved throughout the calculations to ensure the final answer has the correct unit of volume.