The rectangular cuboid, or just cuboid, is a three-dimensional shape that consists of six rectangles. Each rectangle is called a face. Every rectangular cuboid has six faces (The top and bottom faces are often called the top and bottom bases of the rectangular cuboid). It is important to understand that there are actually 3 pairs of faces, and each face will be identical to its opposite face.
The straight lines formed by two intersecting sides are called edges (or sides). Every cuboid has 12 edges.
The meeting point between two edges is called the vertex. Each cuboid has 8 vertices.
Calculate the surface area of the orthohedron below using the data in the diagram.
Incorrect
Correct Answer:
62
Question 3
Calculate the volume of the rectangular prism below using the data provided.
Incorrect
Correct Answer:
48
Question 4
Calculate the volume of the rectangular prism below using the data provided.
Incorrect
Correct Answer:
180
Question 5
A rectangular prism has a base measuring 5 units by 8 units.
The height of the prism is 12 units.
Calculate its volume.
Incorrect
Correct Answer:
480
Examples with solutions for Cuboids
Exercise #1
Look at the cuboid below:
What is the volume of the cuboid?
Video Solution
Step-by-Step Solution
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×w×h
Step 3: Substitute the given dimensions into the formula and calculate:
V=12×8×5
Step 4: Perform the multiplication in stages for clarity:
First, calculate 12×8=96
Then multiply the result by 5: 96×5=480
Therefore, the volume of the cuboid is 480cm3.
Answer
480 cm³
Exercise #2
Calculate the surface area of the orthohedron below using the data in the diagram.
Video Solution
Step-by-Step Solution
To solve this problem, we'll utilize the formula for the surface area of a cuboid. The steps are as follows:
Step 1: Identify the dimensions from the problem. The dimensions provided are a=3, b=5, and c=2.
Step 2: Apply the surface area formula for a cuboid. The formula is:
2(ab+bc+ac)
where a, b, and c are the dimensions of the cuboid.
Step 3: Substitute the known values into the formula:
2(3⋅5+5⋅2+3⋅2)
Step 4: Calculate each term inside the parentheses:
- a⋅b=3⋅5=15
- b⋅c=5⋅2=10
- a⋅c=3⋅2=6
Step 5: Sum the results from Step 4:
15+10+6=31
Step 6: Multiply the sum by 2 to find the total surface area:
2×31=62
Thus, after performing the necessary calculations, the surface area of the orthohedron is 62 square units.
Answer
62
Exercise #3
Calculate the volume of the rectangular prism below using the data provided.
Video Solution
Step-by-Step Solution
To solve this problem, we'll follow these steps:
Identify the given dimensions of the rectangular prism.
Use the formula for volume: V=l×w×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×w×h=3×8×2.
Step 3: Performing the multiplication, we obtain V=3×8×2=24×2=48.
Therefore, the volume of the rectangular prism is 48.
Answer
48
Exercise #4
Calculate the volume of the rectangular prism below using the data provided.
Video Solution
Step-by-Step Solution
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×w×d.
Step 3: Plugging in our values, we have V=5×4×9=180
Therefore, the volume of the rectangular prism is 180.
Answer
180
Exercise #5
A rectangular prism has a base measuring 5 units by 8 units.
The height of the prism is 12 units.
Calculate its volume.
Step-by-Step Solution
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: Volume=length×width×height
Step 3: Substitute the given dimensions into the formula: Volume=5×8×12
Now, perform the calculation: 5×8=40 40×12=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.
Answer
480
Question 1
Look at the cuboid below.
What is the surface area of the cuboid?
Incorrect
Correct Answer:
392 cm²
Question 2
A cuboid is shown below:
What is the surface area of the cuboid?
Incorrect
Correct Answer:
62
Question 3
Below is a cuboid with a length of
8 cm.
Its width is 2 cm and its height is
4 cm.
Calculate the volume of the cube.
Incorrect
Correct Answer:
64 cm³
Question 4
A cuboid has a length of is 9 cm.
It is 4 cm wide and 5 cm high.
Calculate the volume of the cube.
Incorrect
Correct Answer:
180 cm³
Question 5
Look at the the cuboid below.
What is its surface area?
Incorrect
Correct Answer:
158
Exercise #6
Look at the cuboid below.
What is the surface area of the cuboid?
Video Solution
Step-by-Step Solution
Let's see what rectangles we have:
8*5
8*12
5*12
Let's review the formula for the surface area of a rectangular prism:
(length X width + length X height + width X height) * 2
Now let's substitute all this into the exercise:
(8*5+12*8+12*5)*2= (40+96+60)*2= 196*2= 392
This is the solution!
Answer
392 cm²
Exercise #7
A cuboid is shown below:
What is the surface area of the cuboid?
Video Solution
Step-by-Step Solution
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
Answer
62
Exercise #8
Below is a cuboid with a length of
8 cm.
Its width is 2 cm and its height is
4 cm.
Calculate the volume of the cube.
Video Solution
Step-by-Step Solution
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=8cm, width W=2cm, and height H=4cm.
Step 2: We'll use the formula to calculate the volume of a cuboid: V=L×W×H.
Step 3: Substitute the given dimensions into the formula:
V=8×2×4
Calculate the result:
V=16×4=64
Thus, the volume of the cuboid is 64cm3.
Therefore, the solution to the problem is 64cm3.
Answer
64 cm³
Exercise #9
A cuboid has a length of is 9 cm.
It is 4 cm wide and 5 cm high.
Calculate the volume of the cube.
Video Solution
Step-by-Step Solution
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=length×width×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=length×width×height
Step 3: Substitute the values into the formula: V=9cm×4cm×5cm
Calculate the product: V=180cm3
Therefore, the volume of the cuboid is 180cm3.
Answer
180 cm³
Exercise #10
Look at the the cuboid below.
What is its surface area?
Video Solution
Step-by-Step Solution
First, we recall the formula for the surface area of a cuboid:
(width*length + height*width + height*length) *2
As in the cuboid the opposite faces are equal to each other, the given data is sufficient to arrive at a solution.
We replace the data in the formula:
(8*5+3*5+8*3) *2 =
(40+15+24) *2 =
79*2 =
158
Answer
158
Question 1
Look at the cuboid below.
What is its surface area?
Incorrect
Correct Answer:
150
Question 2
A cuboid has the dimensions shown in the diagram below.
Which rectangles form the cuboid?
Incorrect
Correct Answer:
Two 5X6 rectangles
Two 3X5 rectangles
Two 6X3 rectangles
Question 3
Identify the correct 2D pattern of the given cuboid:
Incorrect
Correct Answer:
Question 4
Calculate the volume of the cuboid
If its length is equal to 7 cm:
Its width is equal to 3 cm:
Its height is equal to 5 cm:
Incorrect
Correct Answer:
105 cm³
Question 5
Given the cuboid of the figure:
What is its volume?
Incorrect
Correct Answer:
180
Exercise #11
Look at the cuboid below.
What is its surface area?
Video Solution
Step-by-Step Solution
We identified that the faces are
3*3, 3*11, 11*3 As the opposite faces of an cuboid are equal, we know that for each face we find there is another face, therefore:
3*3, 3*11, 11*3
or
(3*3, 3*11, 11*3 ) *2
To find the surface area, we will have to add up all these areas, therefore:
(3*3+3*11+11*3 )*2
And this is actually the formula for the surface area!
We calculate:
(9+33+33)*2
(75)*2
150
Answer
150
Exercise #12
A cuboid has the dimensions shown in the diagram below.
Which rectangles form the cuboid?
Video Solution
Step-by-Step Solution
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
Answer
Two 5X6 rectangles
Two 3X5 rectangles
Two 6X3 rectangles
Exercise #13
Identify the correct 2D pattern of the given cuboid:
Step-by-Step Solution
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.
Answer
Exercise #14
Calculate the volume of the cuboid
If its length is equal to 7 cm:
Its width is equal to 3 cm:
Its height is equal to 5 cm:
Video Solution
Step-by-Step Solution
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
Answer
105 cm³
Exercise #15
Given the cuboid of the figure:
What is its volume?
Video Solution
Step-by-Step Solution
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: Volume=length×width×height.
Step 3: Substituting the identified dimensions into the formula, we have: Volume=9×5×4.
Calculating this, we find: 9×5=45, 45×4=180.
Therefore, the volume of the cuboid is 180 cubic units.