A cuboid has the dimensions shown in the diagram below. Which rectangles form the cuboid? 3 3 3 5 5 5 6 6 6

Two 5X6 rectangles Two 3X5 rectangles Two 6X3 rectangles

Three 3X6 rectangles Three 3X5 rectangles

Three 5X6 rectangles Two 3X5 rectangles One 6X3 rectangle

Two 5X3 rectangles Four 3X6 rectangles

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

Cuboid Practice Problems: Volume and Surface Area

Master cuboid calculations with step-by-step practice problems. Learn volume and surface area formulas for rectangular prisms with real-world examples.

📚Master Cuboid Calculations Through Guided Practice

Calculate volume using length × width × height formula
Find total surface area of all six rectangular faces
Solve for missing dimensions using given volume or surface area
Apply percentage calculations to cuboid dimension problems
Work with variables and algebraic expressions in 3D geometry
Identify real-world applications of cuboid calculations

Understanding Cuboids

Complete explanation with examples

Structure of a rectangular cuboid

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.

Detailed explanation

Practice Cuboids

Test your knowledge with 64 quizzes

Identify the correct 2D pattern of the given 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

What is the formula for finding the volume of a cuboid?

The volume of a cuboid is calculated by multiplying its three dimensions: Volume = Length × Width × Height. For example, a cuboid with dimensions 4cm × 3cm × 5cm has a volume of 60 cm³.

How do you calculate the total surface area of a cuboid?

The total surface area formula is S = 2(W×L + H×W + H×L), where you calculate the area of each pair of opposite faces and add them together. This includes all six rectangular faces of the cuboid.

What's the difference between a cuboid and a rectangular prism?

There is no difference - they are the same shape with different names. Other terms include orthohedron, rectangular parallelepiped, and orthogonal parallelepiped. All describe a 3D shape with 6 faces, 12 edges, and 8 vertices.

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

A cuboid has: • 6 faces (all rectangles) • 12 edges (straight lines where faces meet) • 8 vertices (corner points where edges meet). The faces come in three pairs of identical opposite rectangles.

Can you find a missing dimension if you know the volume and two other dimensions?

Yes, you can rearrange the volume formula. If Volume = L × W × H, then Height = Volume ÷ (Length × Width). This method works for finding any missing dimension when you have the volume and the other two measurements.

What are some real-world examples of cuboids?

Common cuboid examples include: 1. Shoeboxes and cereal boxes 2. Smartphones and tablets 3. Rooms and buildings 4. Books and bricks 5. Refrigerators and washing machines. Understanding cuboid calculations helps with packing, construction, and space planning.

How do you calculate surface area without the top and bottom faces?

To find lateral surface area (without bases), use the formula: Ss = 2(W×H + L×H). This calculates only the four rectangular faces that 'wrap around' the cuboid, excluding the top and bottom faces.

What's the easiest way to remember cuboid formulas?

Remember these key patterns: Volume always multiplies all three dimensions (L×W×H). Surface area adds up rectangular face areas, with each face appearing twice since opposite faces are identical. Practice with simple whole numbers first before tackling complex problems.

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Applying the formula A shape consisting of several shapes (requiring the same formula) Calculate The Missing Side based on the formula Calculation using percentages Data with powers and roots Extended distributive law Finding Area based off Perimeter and Vice Versa How many times does the shape fit inside of another shape? Identifying and defining elements Identify the greater value Increasing a specific element by addition of.....or multiplication by....... Subtraction or addition to a larger shape Suggesting options for terms when the formula result is known Using additional geometric shapes Using congruence and similarity Using Pythagoras' theorem Using ratios for calculation Using variables Worded problems Applying the formula A shape consisting of several shapes (requiring the same formula) Calculate The Missing Side based on the formula Calculation using percentages Finding Area based off Perimeter and Vice Versa How many times does the shape fit inside of another shape? Subtraction or addition to a larger shape Using Pythagoras' theorem Using ratios for calculation Using variables Verifying whether or not the formula is applicable Worded problems

Cuboid Practice Problems: Volume and Surface Area

Understanding Cuboids

Structure of a rectangular cuboid

Practice Cuboids

Examples with solutions for Cuboids

Frequently Asked Questions

What is the formula for finding the volume of a cuboid?

How do you calculate the total surface area of a cuboid?

What's the difference between a cuboid and a rectangular prism?

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

Can you find a missing dimension if you know the volume and two other dimensions?

What are some real-world examples of cuboids?

How do you calculate surface area without the top and bottom faces?

What's the easiest way to remember cuboid formulas?

More Cuboids Questions

Volume of a Orthohedron

Cuboids

Surface Area of a Cuboid

Practice by Question Type

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