Identify the correct 2D pattern of the given cuboid: 4 4 4 4 4 4 9 9 9

9 9 9 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

4 4 4 4 4 4 9 9 9 4 4 4 4 4 4 4 4 4 4 4 4

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 9 9 9 4 4 4 9 9 9

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 9 9 9

An orthohedron has the dimensions: 4, 7, 10. How many rectangles is it formed of and what are their dimensions?

2 Rectangles 4X7 2 Rectangles 4X10 2 Rectangles 7X10

2 Rectangles 10X7 2 Rectangles 10X4 2 square 10X10

2 Rectangles 10X7 2 Rectangles 7X4

3 Rectangles 10X7 3 Rectangles 4X7

Cuboids Practice Problems & Three-Dimensional Figures

Master cuboids, cylinders, and prisms with step-by-step practice problems. Calculate volume, surface area, and lateral area of 3D shapes with detailed solutions.

📚Practice Three-Dimensional Figures and Build Your Geometry Skills

Calculate volume of cuboids using length × width × height formula
Find surface area of rectangular prisms with complete step-by-step solutions
Determine lateral area of cuboids excluding the top and bottom faces
Solve cylinder volume problems using πr²h formula with real measurements
Calculate total surface area of cylinders including bases and lateral surface
Work with triangular prism volume and area calculations

Understanding Cuboids

Complete explanation with examples

Three-dimensional figures

What are three-dimensional figures?

So far we have worked with common two-dimensional figures such as the square or the triangle.
Three-dimensional figures are those that extend into the third dimension, meaning that in addition to length and width, they also have height (that is, the figure has depth).

What differences do three-dimensional figures have?

Three-dimensional figures have several definitions that we will see next:
Below is a three-dimensional figure that we will use to learn each definition - The cube:

Face: it is the flat side of a three-dimensional figure
In the cube we have here, there are 6 faces (one of them is painted gray)
Edge: these are the lines that connect one face to another in a three-dimensional figure
In the cube we have here, there are 12 edges (painted green)
Vertex: it is the point that connects the edges
In the cube we have here, there are 8 vertices (painted orange)

Volume: it is the amount of space contained within a three-dimensional figure.
The units of measurement are $cm^3$ .

Detailed explanation

Practice Cuboids

Test your knowledge with 25 quizzes

A cuboid has the dimensions shown in the diagram below.

Which rectangles form the cuboid?

Examples with solutions for Cuboids

Step-by-step solutions included

Exercise #1

Look at the cuboid below:

What is the volume of the cuboid?

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:

$V = l \times w \times h$

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

Answer:

480 cm³

Video Solution

Exercise #2

Look at the cuboid below.

What is the surface area of the cuboid?

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

Video Solution

Exercise #3

A cuboid is shown below:

What is the surface area of the cuboid?

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:

Video Solution

Exercise #4

Given the cuboid of the figure:

What is its volume?

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:
$\text{Volume} = \text{length} \times \text{width} \times \text{height}.$

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.

Answer:

180

Video Solution

Exercise #5

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:

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

Video Solution

Frequently Asked Questions

Everything you need to know about Cuboids

How do you calculate the volume of a cuboid step by step?

To find the volume of a cuboid, multiply length × width × height. For example, if a cuboid has dimensions 5 cm × 3 cm × 4 cm, the volume is 5 × 3 × 4 = 60 cm³. Always include cubic units in your final answer.

What is the difference between surface area and lateral area of a cuboid?

Surface area includes all 6 faces of the cuboid using the formula 2(lw + hw + hl). Lateral area only includes the 4 side rectangles, excluding the top and bottom, calculated as 2h(l + w).

How many faces, edges, and vertices does a cuboid have?

A cuboid has: • 6 faces (rectangles that form the surface) • 12 edges (lines where faces meet) • 8 vertices (corner points where edges connect)

What is the formula for cylinder volume and when do you use it?

The cylinder volume formula is V = πr²h, where r is the radius of the circular base and h is the height. Use this when you need to find how much space is inside a cylindrical container or object.

How do you find the total surface area of a cylinder?

Use the formula: Total Surface Area = 2πrh + 2πr². This includes the lateral (curved) surface area (2πrh) plus the area of both circular bases (2πr²). Remember to use π ≈ 3.14 in calculations.

What makes a triangular prism different from other 3D shapes?

A triangular prism has 2 identical triangular bases connected by 3 rectangular faces. Unlike cuboids with all rectangular faces, or cylinders with circular bases, triangular prisms combine triangular and rectangular surfaces.

When solving 3D geometry problems, what measurements do I need?

For cuboids: length, width, height For cylinders: radius (or diameter) and height For triangular prisms: base triangle measurements and prism height Always check which specific calculation (volume, surface area, or lateral area) is required.

How do face diagonals differ from space diagonals in a cuboid?

Face diagonals connect two vertices on the same rectangular face of the cuboid. Space diagonals (also called body diagonals) connect vertices from opposite corners of the entire cuboid, passing through the interior space.

Cuboids Practice Problems & Three-Dimensional Figures

Understanding Cuboids

Three-dimensional figures

What are three-dimensional figures?

What differences do three-dimensional figures have?

Practice Cuboids

Examples with solutions for Cuboids

Frequently Asked Questions

How do you calculate the volume of a cuboid step by step?

What is the difference between surface area and lateral area of a cuboid?

How many faces, edges, and vertices does a cuboid have?

What is the formula for cylinder volume and when do you use it?

How do you find the total surface area of a cylinder?

What makes a triangular prism different from other 3D shapes?

When solving 3D geometry problems, what measurements do I need?

How do face diagonals differ from space diagonals in a cuboid?

More Cuboids Questions

Cuboids

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