Cuboid Practice Problems: Volume and Surface Area

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 $180 \, \text{cm}^3$.

Every cuboid is made up of rectangles. These rectangles are the faces of the cuboid.

As we know that in a rectangle the parallel faces are equal to each other, we can conclude that for each face found there will be two rectangles.

Let's first look at the face painted orange,

It has width and height, 5 and 3, so we already know that they are two rectangles of size 5x6

Now let's look at the side faces, they also have a height of 3, but their width is 6,

And then we understand that there are two more rectangles of 3x6

Now let's look at the top and bottom faces, we see that their dimensions are 5 and 6,

Therefore, there are two more rectangles that are size 5x6

That is, there are
2 rectangles 5X6

2 rectangles 3X5

2 rectangles 6X3

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: $\text{180 cm}^3$.

Remember that the formula for the surface area of a cuboid is:

(length X width + length X height + width X height) 2

We input the known data into the formula:

2*(3*2+2*5+3*5)

2*(6+10+15)

2*31 = 62

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: $480$.