Volume of a Orthohedron: Verifying whether or not the formula is applicable

To solve this problem, we must use the volume formula for a cuboid, which requires the length, width, and height. The given dimensions are:

• Width ($w$) = 5 cm
• Height ($h$) = 7 cm

The formula for the volume of a cuboid is $V = l \times w \times h$, where $l$ represents the length, $w$ the width, and $h$ the height.

Based on the problem statement, only the width and height of the cuboid are provided. The length ($l$) is not specified. Therefore, it is not possible to calculate the volume of the cuboid without the third dimension. Thus, we cannot use the volume formula as it requires all three dimensions.

Therefore, it is not possible to calculate the volume of the cuboid with the information given.

The correct answer is No.

To solve this problem, we recognize that calculating the volume of a cuboid requires three dimensions: length, width, and height.

• Step 1: Identify the given dimensions—height is 8 cm, and length is 5 cm.
• Step 2: Note that the width of the cuboid is not provided.
• Step 3: Recall the volume formula for a cuboid: $V = \text{length} \times \text{width} \times \text{height}$.
• Step 4: Attempt to apply the formula: Without the width, the formula is incomplete.

Given the absence of the width, it is impossible to perform the calculation for the volume. All three dimensions must be known to determine the volume of a cuboid.

Therefore, the solution to the problem is No.

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

• Identify the given information about the cuboid's dimensions.
• Apply the appropriate formula for calculating the volume.

Now, let's work through each step:

The given dimensions are: height ($h$) = 9 cm, length ($l$) = 6 cm, and width ($w$) = 8 cm.

The formula for the volume of a cuboid is:

$V = l \times w \times h$

Substitute the given values into the formula:

$V = 6 \, \text{cm} \times 8 \, \text{cm} \times 9 \, \text{cm}$

We can carry out this multiplication to actually find the volume, which would result in a number, but the problem only asks us if it's possible to calculate the volume. Since we have all dimensions necessary and we've correctly applied the formula, it is indeed possible to calculate the volume.

Therefore, the answer is:

Yes

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

• Step 1: Calculate the side length of the square base.
• Step 2: Calculate the area of the square base.
• Step 3: Compute the volume of the cuboid using the area and height.

Let's work through each step:

Step 1: The perimeter of the square base is given as 12 cm. We can find the side length $s$ of the square using the perimeter formula:

$P = 4s$

So,

$12 = 4s$ which implies $s = \frac{12}{4} = 3 \text{ cm}$.

Step 2: The area of the square base is then:

$\text{Area} = s^2 = 3^2 = 9 \text{ cm}^2$.

Step 3: To find the volume of the cuboid, we use the formula for volume:

$V = \text{Base Area} \times \text{Height} = 9 \times 8 = 72 \text{ cm}^3$.

Thus, we have successfully determined that it is possible to calculate the volume of the cuboid, and the volume is $72 \text{ cm}^3$.

Therefore, the correct answer to the problem is Yes.

To solve this problem, let's go through the steps:

• Step 1: Determine the side length of the square base.
• Step 2: Note that calculating the volume requires the height of the cuboid, which is not given.

Now, let's perform these steps:

Step 1: We know the perimeter of the square base is 24 cm. The formula for the perimeter of a square is:

$P = 4s$

where $s$ is the side length of the square. Thus:

$24 = 4s$

Solving for $s$, we find:

$s = \frac{24}{4} = 6 \, \text{cm}$

Step 2: To find the volume of the cuboid, we use the formula:

$V = \text{Base Area} \times \text{Height}$

The base area $A$ is:

$A = s^2 = 6^2 = 36 \, \text{cm}^2$

However, the height $h$ of the cuboid is not provided, which is essential to calculate the volume.

Conclusion: Since the height of the cuboid is unknown, it is impossible to calculate the volume of the cuboid.

Therefore, the solution to the problem is No.

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

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula for the volume of the cuboid.
• Step 3: Perform the necessary substitution.

Now, let's work through each step:
Step 1: The problem gives us the area of the base, which is 16 cm$^2$, and the height of the cuboid, which is 6 cm.
Step 2: The formula to find the volume of a cuboid is given by:

$V = \text{Base Area} \times \text{Height}$

Step 3: Substitute the given values into the formula:

$V = 16 \, \text{cm}^2 \times 6 \, \text{cm}$

After substituting, we find that $V = 96 \, \text{cm}^3$.

This means it is indeed possible to calculate the volume of the cuboid given the area of the base and the height.

Therefore, the answer is Yes.