Cuboid Practice Problems: Volume and Surface Area

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: $480$.

Let's go through the options:

A - In this option, we can observe that there are two flaps on the same side.

If we try to turn this net into a box, we should obtain a box where on one side there are two faces one on top of the other while the other side is "open",
meaning this net cannot be turned into a complete and full box.

B - This net looks valid at first glance, but we need to verify that it matches the box we want to draw.

In the original box, we see that we have four flaps of size 9*4, and only two flaps of size 4*4,
if we look at the net we can see that the situation is reversed, there are four flaps of size 4*4 and two flaps of size 9*4,
therefore we can conclude that this net is not suitable.

C - This net at first glance looks valid, it has flaps on both sides so it will close into a box.

Additionally, it matches our drawing - it has four flaps of size 9*4 and two flaps of size 4*4.

Therefore, we can conclude that this net is indeed the correct net.

D - In this net we can see that there are two flaps on the same side, therefore this net will not succeed in becoming a box if we try to create it.

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