Free Volume Worksheets: Surface Area & Finding Volume - Free Printable

Problem Description:

The task is to calculate the volume of each 3D shape shown in the image. The shapes are cubes and rectangular prisms, and we need to use the correct units for our answers.

Step-by-Step Solution:

#### Shape 1: Cube
- Dimensions: Side length = 4 cm
- Formula for Volume of a Cube:
\[
V = \text{side}^3
\]
- Calculation:
\[
V = 4^3 = 4 \times 4 \times 4 = 64 \, \text{cm}^3
\]

#### Shape 2: Rectangular Prism
- Dimensions: Length = 2 cm, Width = 2 cm, Height = 6 cm
- Formula for Volume of a Rectangular Prism:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
- Calculation:
\[
V = 2 \times 2 \times 6 = 4 \times 6 = 24 \, \text{cm}^3
\]

#### Shape 3: Rectangular Prism
- Dimensions: Length = 10 cm, Width = 3 cm, Height = 3 cm
- Formula for Volume of a Rectangular Prism:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
- Calculation:
\[
V = 10 \times 3 \times 3 = 30 \times 3 = 90 \, \text{cm}^3
\]

#### Shape 4: Rectangular Prism
- Dimensions: Length = 12 cm, Width = 6 cm, Height = 1 cm
- Formula for Volume of a Rectangular Prism:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
- Calculation:
\[
V = 12 \times 6 \times 1 = 72 \times 1 = 72 \, \text{cm}^3
\]

Final Answers:

1. Cube: \( \boxed{64 \, \text{cm}^3} \)
2. Rectangular Prism (2 cm × 2 cm × 6 cm): \( \boxed{24 \, \text{cm}^3} \)
3. Rectangular Prism (10 cm × 3 cm × 3 cm): \( \boxed{90 \, \text{cm}^3} \)
4. Rectangular Prism (12 cm × 6 cm × 1 cm): \( \boxed{72 \, \text{cm}^3} \)

Explanation:

- Volume of a Cube: Since all sides of a cube are equal, the volume is calculated by cubing the side length.
- Volume of a Rectangular Prism: The volume is found by multiplying the length, width, and height of the prism.
- Units: Since the dimensions are given in centimeters (cm), the volume will be in cubic centimeters (\( \text{cm}^3 \)).

This method ensures accurate calculation for each shape based on their respective formulas.