Cuboids Practice Problems & Three-Dimensional Figures

To determine the feasability of a cuboid composed of two 4x3 rectangles and four 4x4 squares, we start by calculating the total surface area these would provide:

The total surface area contributes as follows:
- Two 4x3 rectangles: $2 \times 4 \times 3 = 24$
- Four 4x4 squares: $4 \times 4 \times 4 = 64$

The total surface area is $24 + 64 = 88$.

When forming a cuboid with dimensions $l \times w \times h$, the surface area should satisfy:
$2(lw + lh + wh) = 88$.

Now, let us examine possible dimensions that can result from the given face dimensions:

• Dimension 1: 4 (from the squares).
  
• Dimension 2: 3 (from the rectangles).
• Dimension 3 needs consideration from remaining panels.

Since using the given two 4x3 rectangles and four 4x4 squares in a valid arrangement providing 6 surface faces does not meet the criteria without repeating or extending beyond six faces, the random assembly of these square and rectangular panels cannot result in a valid orthogonal shape (cuboid).

Conclusively, this orthohedron is not possible.

Thus, the solution is that 'This orthohedron is not possible.'

To solve this problem, we'll follow these steps:

• Step 1: Identify the given dimensions of the cuboid.
• Step 2: Apply the formula for the volume of a cuboid.
• Step 3: Perform the calculation using the known dimensions.

Now, let's work through each step:
Step 1: The problem states that the cuboid has a length of 8 cm, a width of 2 cm, and a height of 4 cm.
Step 2: We will use the volume formula for a cuboid, which is:

$V = \text{length} \times \text{width} \times \text{height}$

Step 3: Substituting the given dimensions into the formula, we have:

$V = 8 \, \text{cm} \times 2 \, \text{cm} \times 4 \, \text{cm}$

Performing the multiplication:

$V = 16 \, \text{cm}^2 \times 4 \, \text{cm} = 64 \, \text{cm}^3$

Therefore, the volume of the cuboid is $64 \, \text{cm}^3$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given dimensions: length = 9 cm, width = 4 cm, height = 5 cm.
• Step 2: Apply the formula for the volume of a cuboid, $V = \text{length} \times \text{width} \times \text{height}$.
• Step 3: Calculate the value by substituting the given dimensions into the formula.

Now, let's work through each step:

Step 1: Given dimensions are:
- Length = 9 cm
- Width = 4 cm
- Height = 5 cm

Step 2: Use the formula for the volume of a cuboid:
$V = \text{length} \times \text{width} \times \text{height}$

Step 3: Substitute the values into the formula:
$V = 9 \, \text{cm} \times 4 \, \text{cm} \times 5 \, \text{cm}$

Calculate the product:
$V = 180 \, \text{cm}^3$

Therefore, the volume of the cuboid is $180 \, \text{cm}^3$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula for volume
• Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: The problem gives us the dimensions of a cuboid: length $L = 8 \, \text{cm}$, width $W = 2 \, \text{cm}$, and height $H = 4 \, \text{cm}$.

Step 2: We'll use the formula to calculate the volume of a cuboid: $V = L \times W \times H$.

Step 3: Substitute the given dimensions into the formula: $V = 8 \times 2 \times 4$ Calculate the result: $V = 16 \times 4 = 64$ Thus, the volume of the cuboid is $64 \, \text{cm}^3$.

Therefore, the solution to the problem is $64 \, \text{cm}^3$.

To determine the volume of a cuboid, we apply the formula:

• Step 1: Identify the dimensions of the cuboid:
  • Length ($l$) = 12 cm
  • Width ($w$) = 8 cm
  • Height ($h$) = 5 cm
• Step 2: Apply the volume formula for a cuboid:

The formula to find the volume ($V$) of a cuboid is:

$V = l \times w \times h$

Step 3: Substitute the given dimensions into the formula and calculate: $V = 12 \times 8 \times 5$

Step 4: Perform the multiplication in stages for clarity:

First, calculate $12 \times 8 = 96$

Then multiply the result by 5: $96 \times 5 = 480$

Therefore, the volume of the cuboid is $\mathbf{480 \, \text{cm}^3}$.