Surface Area of a Cuboid - Examples, Exercises and Solutions

Look at the cuboid below.

What is the surface area of the cuboid?

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!
 

392 cm²

A cuboid is shown below:

What is the surface area of the cuboid?

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

62

Look at the the cuboid below.

What is its surface area?

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

158

Look at the cuboid below.

What is its surface area?

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

150

A cuboid has the dimensions shown in the diagram below.

Which rectangles form the cuboid?

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

Two 5X6 rectangles

Two 3X5 rectangles

Two 6X3 rectangles

An unfolded cuboid is shown below.

What is the surface area of the cuboid?

To calculate the surface area of the rectangular prism, we will need to identify its three faces (each face appears twice):

1*3

1*8

3*8

The formula for the surface area of a rectangular prism is the sum of all the areas of the faces, that is:

We replace the data in the formula:

2*(1*3+1*8+3*8)=
2*(3+8+24) = 
2*35 = 

70

And this is the solution!

70

Which dimensions may represent a cuboid?

There is no limitation or rule regarding the dimensions a box can have,

therefore the correct answer is D

All of the above.

Given that the volume of the cuboid is equal to 72 cm³

The length of the cuboid is equal to 6 cm and the height is equal to half the length.

Calculate the surface of the cuboid

The first step is to calculate the relevant data for all the components of the box.

The length of the box = 6

Given that the height of a cuboid is equal to half its length we are able to deduce the height of the box as follows : 6/2= 3

Hence the height = 3

In order to determine the width, we insert the known data into the formula for the volume of the box:

height*length*width = volume of the cuboid.

3*6*width = 72

18*width=72

We divide by 18:

Hence the width = 4

We are now able to return to the initial question regarding the surface of the cuboid.

Remember that the formula for the surface area is:

(height*length+height*width+length*width)*2

We insert the known data leaving us with the following result:

(3*6+4*3+4*6)*2=

(12+24+18)*2=

(54)*2=

108

108 cm²

Calculate the surface area of the orthohedron below using the data in the diagram.

62

A rectangular prism has a square base measuring 25 cm.

It has a height is equal to 3 cm.

Calculate the surface area of the rectangular prism.

110

Given the cuboid whose square base is of size 25 cm²,

The height of the cuboid is 3 cm,

What is the surface area of the cuboid?

110 cm²

A cuboid has a surface area of 102.

Calculate X.

3

Look at the cuboid of the figure.

Its surface area is 122 cm².

What is the width of the cuboid?

4 cm

The surface area of the cuboid shown below is 147 cm².

What are the dimensions of the cuboid that are not labelled in the drawing?

Impossible to calculate.

The surface area of a cube is 24 cm².

How long are the sides of the cube?

2