Volume of a Orthohedron - Examples, Exercises and Solutions

Students start learning mathematics as early as elementary school, and as they progress, the subject becomes more and more complicated. Among others, the syllabus devotes a part to geometry and requires students to master different shapes and know how to calculate their area and volume. Are you also studying these days how to calculate the volume of a rectangular prism?

Volume of a rectangular prism:

V = length × width × height

A - how to calculate the volume of a rectangular prism

Suggested Topics to Practice in Advance

  1. Parts of a Rectangular Prism

Practice Volume of a Orthohedron

examples with solutions for volume of a orthohedron

Exercise #1

Given the cuboid whose length is equal to 7 cm

Width is equal to 3 cm

The height of the cuboid is equal to 5 cm

Calculate the volume of the cube

333777555

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 #2

Given the cuboid of the figure:

444XXX2.52.52.5

Given: volume of the cuboid is 45

What is the value of X?

Video Solution

Step-by-Step Solution

Volume formula for a rectangular prism:

Volume = length X width X height

 

Therefore, first we will place the data we are given into the formula:

45 = 2.5*4*X

 

We divide both sides of the equation by 2.5:

18=4*X

And now we divide both sides of the equation by 4:

4.5 = X

Answer

4.5

Exercise #3

Look at the following orthohedron:

444

The volume of the orthohedron is 80 cm3 80~cm^3 .

The length of the lateral edge is 4 meters.

What is the area of the base of the orthohedron?
(shaded orange in the diagram)

Video Solution

Step-by-Step Solution

The formula for the volume of a box is height*length*width

In the specific question, we are given the volume and the height,

and we are looking for the area of the base,

As you will remember, the area is length * width

If we replace all the data in the formula, we see that:

4 * the area of the base = 80

Therefore, if we divide by 4 we see that

Area of the base = 20

Answer

20 cm²

Exercise #4

Given the cuboid of the figure:

333151515

The area of the base of the cuboid is 15 cm²,

The length of the lateral edge is 3 cm.

what is the volume of the cuboid

Video Solution

Step-by-Step Solution

To calculate the volume of a cuboid, as we mentioned, we need the length, width, and height.

It is important to note that in the exercise we are given the height and the base area of the cuboid.

The base area is actually the area multiplied by the length. That is, it is the data that contains the two pieces of information we are missing.

Therefore, we can calculate the area by height * base area

15*3 = 45

This is the solution!

Answer

45 cm²

Exercise #5

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

(14+30X)(14+30X)(14+30X)212121151515

Step-by-Step Solution

We use a formula to calculate the volume: height times width times length.

We rewrite the exercise using the existing data:

21×(14+30x)×15= 21\times(14+30x)\times15=

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

(21×14+21×30x)×15= (21\times14+21\times30x)\times15=

We solve the multiplication exercise in parentheses:

(294+630x)×15= (294+630x)\times15=

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

294×15+630x×15= 294\times15+630x\times15=

We solve each of the exercises in parentheses to find the volume:

4,410+9,450x 4,410+9,450x

Answer

4410+9450x 4410+9450x

examples with solutions for volume of a orthohedron

Exercise #1

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

121212888555

Answer

480

Exercise #2

Look at the cuboid below:

888555121212

What is the volume of the cuboid?

Video Solution

Answer

480 cm²

Exercise #3

Calculate the volume of the rectangular prism below using the data provided. 444555999

Video Solution

Answer

180

Exercise #4

Calculate the volume of the rectangular prism below using the data provided.

888333222

Video Solution

Answer

48

Exercise #5

A cuboid has a length of is 9 cm.

It is 4 cm wide and 5 cm high.

Calculate the volume of the cube.

555444999

Video Solution

Answer

180 cm³

examples with solutions for volume of a orthohedron

Exercise #1

A cuboid is 9 cm long, 4 cm wide, and 5 cm high.

Calculate the volume of the cube.

555999444

Video Solution

Answer

180 cm³

Exercise #2

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.

222888444

Video Solution

Answer

64 cm³

Exercise #3

Shown 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.

444888222

Video Solution

Answer

64 cm³

Exercise #4

Given the cuboid of the figure:

555999444

What is its volume?

Video Solution

Answer

180

Exercise #5

The volume of the cuboid is es:

Video Solution

Answer

length X widthX height

Topics learned in later sections

  1. Cuboids
  2. How to calculate the surface area of a rectangular prism (orthohedron)
  3. Cubes