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?

Suggested Topics to Practice in Advance

1. Parts of a Rectangular Prism

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

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

105 cm³

Exercise #2

Given the cuboid of the figure:

Given: volume of the cuboid is 45

What is the value of X?

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

4.5

Exercise #3

Look at the following orthohedron:

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

The length of the lateral edge is 4 meters.

What is the area of the base of the orthohedron?

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

20 cm²

Exercise #4

Given the cuboid of the figure:

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

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!

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.

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:

$21\times(14+30x)\times15=$

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

$(21\times14+21\times30x)\times15=$

We solve the multiplication exercise in parentheses:

$(294+630x)\times15=$

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

$294\times15+630x\times15=$

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

$4,410+9,450x$

$4410+9450x$

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.

480

Exercise #2

Look at the cuboid below:

What is the volume of the cuboid?

480 cm²

Exercise #3

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

180

Exercise #4

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

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.

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.

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.

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.

64 cm³

Exercise #4

Given the cuboid of the figure:

What is its volume?

180

Exercise #5

The volume of the cuboid is es: