Question

the solid below is made from cubes. find its volume. 1 m
□ m³

Explanation:

Step1: Determine the side length of each small cube

From the diagram, the length of 2 small cubes is 1 m, so the side length of each small cube, \( s \), is \( \frac{1}{2} = 0.5 \) m.

Step2: Determine the number of cubes along each dimension

• Along the length: By counting the cubes, we can see there are 6 cubes.
• Along the width: There are 2 cubes.
• Along the height: There are 4 cubes.

Step3: Calculate the volume of one small cube

The volume of a cube is given by \( V_{small} = s^3 \). Substituting \( s = 0.5 \) m, we get \( V_{small} = (0.5)^3 = 0.125 \) \( m^3 \).

Step4: Calculate the total number of small cubes

The total number of small cubes, \( N \), is the product of the number of cubes along each dimension. So \( N = 6 \times 2 \times 4 = 48 \).

Step5: Calculate the volume of the solid

The volume of the solid, \( V \), is the product of the volume of one small cube and the total number of small cubes. So \( V = N \times V_{small} = 48 \times 0.125 = 6 \) \( m^3 \).

Alternatively, we can use the dimensions of the rectangular prism formed by the cubes. The length of the prism, \( l = 6 \times 0.5 = 3 \) m, the width, \( w = 2 \times 0.5 = 1 \) m, and the height, \( h = 4 \times 0.5 = 2 \) m. Then the volume of a rectangular prism is \( V = l \times w \times h \), so \( V = 3 \times 1 \times 2 = 6 \) \( m^3 \).

Answer:

\( 6 \) \( m^3 \)