Volume of a Orthohedron: Applying the formula

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 $\mathbf{480 \, \text{cm}^3}$.

To solve this problem, we'll calculate the volume of the cuboid using the given dimensions:

• Step 1: Identify the dimensions
• Step 2: Apply the volume formula for a cuboid
• Step 3: Calculate the volume

Let's work through these steps:

Step 1: From the diagram, we are informed of two dimensions directly: the width $w = 5$ and the height $h = 4$. The diagram also indicates the horizontal length (along the base) is $l = 9$.

Step 2: To find the volume of the cuboid, we use the formula:
$\text{Volume} = \text{length} \times \text{width} \times \text{height}.$

Step 3: Substituting the identified dimensions into the formula, we have:
$\text{Volume} = 9 \times 5 \times 4.$

Calculating this, we find:
$9 \times 5 = 45,$
$45 \times 4 = 180.$

Therefore, the volume of the cuboid is $180$ cubic units.

This corresponds to choice \#4: 180.

The formula to calculate the volume of a cuboid is:

height*length*width

We replace the data in the formula:  

3*5*7

7*5 = 35

35*3 = 105

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 calculate the volume of the cuboid, we apply the formula for the volume of a cuboid:

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

Given:

• Length = 9 cm
• Width = 4 cm
• Height = 5 cm

Now, substituting the values into the formula:

$V = 9 \times 4 \times 5$

First, multiply 9 and 4:

$9 \times 4 = 36$

Then, multiply the result by 5:

$36 \times 5 = 180$

Therefore, the volume of the cuboid is 180 cm³.

Since this is a multiple-choice question, the correct choice is 4: $\text{180 cm}^3$.

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 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:

• Identify the given dimensions of the rectangular prism.
• Use the formula for volume: $V = l \times w \times h$.
• Calculate the volume by plugging in the given values.

Now, let's work through each step:
Step 1: The problem provides the dimensions of the prism: length = 3, width = 8, height = 2.
Step 2: Applying the formula, we have $V = l \times w \times h = 3 \times 8 \times 2$.
Step 3: Performing the multiplication, we obtain $V = 3 \times 8 \times 2 = 24 \times 2 = 48$.

Therefore, the volume of the rectangular prism is $48$.

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

• Step 1: Identify the given dimensions of the prism.
• Step 2: Apply the formula for the volume of a rectangular prism.
• Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: The given dimensions are height $h = 5$, width $w = 4$, and depth $d = 9$.
Step 2: We use the formula for volume $V = h \times w \times d$.
Step 3: Plugging in our values, we have
$V = 5 \times 4 \times 9 = 180$

Therefore, the volume of the rectangular prism is $180$.

To solve this problem, we need to find the volume of the rectangular prism by following these steps:

• Step 1: Identify the given dimensions.
• Step 2: Apply the formula for the volume of a rectangular prism.
• Step 3: Plug in the values and calculate the volume.

Let's proceed with each step:

Step 1: We are given the length = 5 units, width = 8 units, and height = 12 units of the prism.

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

Step 3: Substitute the given dimensions into the formula:
$\text{Volume} = 5 \times 8 \times 12$

Now, perform the calculation:
$5 \times 8 = 40$
$40 \times 12 = 480$

Thus, the volume of the rectangular prism is $480$ cubic units.

Therefore, the correct choice from the given options, based on this calculation, is Choice 3: $480$.

To calculate the volume of a cuboid, as we mentioned, we need the length, width, and height.

It is important to note that in the exercise we are given the height and the base area of the cuboid.

The base area is actually the area multiplied by the length. That is, it is the data that contains the two pieces of information we are missing.

Therefore, we can calculate the area by height * base area

15*3 = 45

This is the solution!

To solve the problem of finding the volume of the given cuboid, we'll follow the outlined steps:

• Step 1: Calculate the area of the base.
• Step 2: Multiply the base area by the height to find the volume.

Now, let's work through each step:

Step 1: Calculate the area of the base.
The side length of the square base is given as 8 cm. The formula for the area of a square is $a^2$, where $a$ is the side length. Substituting the value, we get:
$\text{Base Area} = 8^2 = 64 \, \text{cm}^2$

Step 2: Multiply the base area by the height.
The height of the cuboid is given as 5 cm. Using the formula for the volume of a cuboid $\text{Volume} = \text{Base Area} \times \text{Height}$, we substitute the known values:
$\text{Volume} = 64 \, \text{cm}^2 \times 5 \, \text{cm} = 320 \, \text{cm}^3$

Therefore, the volume of the cuboid is $320 \, \text{cm}^3$.

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

• Step 1: Identify the given dimensions: length, width, and height.
• Step 2: Apply the volume formula for a cuboid.
• Step 3: Perform the multiplication to find the volume.
• Step 4: Match the result with the provided choices to confirm the correct answer.

Now, let's work through each step:
Step 1: We are given the cuboid's dimensions: length = 8 cm, width = 10 cm, height = 9 cm.
Step 2: To find the volume $V$ of the cuboid, we use the formula:
$V = \text{length} \times \text{width} \times \text{height}$.
Step 3: Substitute the given values into the formula:
$V = 8 \, \text{cm} \times 10 \, \text{cm} \times 9 \, \text{cm}$.
Calculate the product:
$V = 8 \times 10 \times 9 = 720 \, \text{cm}^3$.
Step 4: The calculated volume is $720 \, \text{cm}^3$, which matches choice 4.

Therefore, the solution to the problem is $720 \, \text{cm}^3$.

To solve this problem, we follow these steps:

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

Now, let's work through each step:
Step 1: The problem gives us the following dimensions for the cuboid: length = 15 cm, width = 16 cm, and height = 10 cm.
Step 2: We'll use the formula for the volume of a cuboid: $V = l \times w \times h$.
Step 3: Substituting in the values, we get: $V = 15 \times 16 \times 10$.
Calculating this, we find that:
$V = 15 \times 16 \times 10 = 2400$ cubic centimeters.

Therefore, the volume of the cuboid is $2400 \, \text{cm}^3$, which corresponds to choice 2 in the given options.