What does the angle in the figure represent? A A A B B B F F F E E E D D D C C C G G G H H H

The angle between two diagonals of the rectangular prism.

An angle that, if added to angle HEG, gives us 180 degrees.

Parts of a Cuboid: Identifying and defining elements

Question 1

The volume of the cuboid is es:

Question 2

How many edges does a cuboid have?

Question 3

Identify which of the following line segments is the diagonal of the rectangular prism?

Question 4

Look at the dotted diagonal in the figure below.

Which diagonals of the rectangular prism are equal?

Question 5

Look at the cuboid in the figure.

Which of the following is an edge of the given cuboid?

Examples with solutions for Parts of a Cuboid: Identifying and defining elements

Exercise #1

The volume of the cuboid is es:

Video Solution

Step-by-Step Solution

To solve this problem, we need to identify the correct formula for the volume of a cuboid:

A cuboid is defined by three dimensions: length ( $l$ ), width ( $w$ ), and height ( $h$ ). To find the volume of a cuboid, we use the formula:

$V = l \times w \times h$

Given the answer choices:

Choice 1: $l \times 2 \times w$
Choice 2: $l \times w \times h$
Choice 3: $l \times w$
Choice 4: $w \times h$

The formula for the volume of a cuboid is explicitly listed in Choice 2, which is $l \times w \times h$ . This matches the standard mathematical formula for volume.

Thus, the correct answer to the problem is Choice 2: $\text{length } \times \text{width } \times \text{height}$ .

Answer

length X widthX height

Exercise #2

How many edges does a cuboid have?

Video Solution

Step-by-Step Solution

"Edges" is the name of the box's sides. Since a box is a three-dimensional shape, we call these parts edges.

Counting the edges of a box, we can see that there arehas 12 edges:

Answer

$12$

Exercise #3

Identify which of the following line segments is the diagonal of the rectangular prism?

Video Solution

Step-by-Step Solution

A box diagonal is a diagonal that passes between two vertices that are not connected,
meaning, the diagonal passes through the box, and not on one of its edges.

Let's see which of the segments in the answers passes entirely through the box from end to end.

AC, HF and FC are all diagonals that lie on the edges of the box, therefore the segment that fits this description is BH.

Answer

$BH$

Exercise #4

Look at the dotted diagonal in the figure below.

Which diagonals of the rectangular prism are equal?

Video Solution

Step-by-Step Solution

Let's look at the face AEHD

In it, there is another diagonal equal to ED, which is AH

Let's look at the face BFGC which is identical and equal to AEHD, in which there are two diagonals that are also equal to ED:

$FC=BG=ED$

Answer

$AH,BG,FC$

Exercise #5

Look at the cuboid in the figure.

Which of the following is an edge of the given cuboid?

Video Solution

Answer

Question 1

The quadrilateral of the cuboid is:

Question 2

The number of faces in the cuboid is:

Question 3

How many diagonals identical to the dotted diagonal in the diagram are there in the rectangular prism?

Question 4

The number of vertices in the cuboid is:

Question 5

Which is the longest line indicated in the diagram?

Exercise #6

The quadrilateral of the cuboid is:

Video Solution

Answer

Rectangle

Exercise #7

The number of faces in the cuboid is:

Video Solution

Answer

$6$

Exercise #8

How many diagonals identical to the dotted diagonal in the diagram are there in the rectangular prism?

Video Solution

Answer

$4$

Exercise #9

The number of vertices in the cuboid is:

Video Solution

Answer

$8$

Exercise #10

Which is the longest line indicated in the diagram?

Video Solution

Answer

$c$

Question 1

Look at the cuboid below.

Which of the following answers is a face of the given cuboid?

Question 2

Choose the dimensions that represent an orthohedron with a square base.

Question 3

Choose the dimensions that represent an orthohedron with a square base.

Question 4

The combined size of the angles between two edges of the cuboid is...?

Question 5

Look at the orthohedron in the figure below.

Which angle is between the diagonal BH and the face ABFE?

Exercise #11

Look at the cuboid below.

Which of the following answers is a face of the given cuboid?

Video Solution

Answer

EFHG

Exercise #12

Choose the dimensions that represent an orthohedron with a square base.

Video Solution

Answer

$12,12,12$

Exercise #13

Choose the dimensions that represent an orthohedron with a square base.

Video Solution

Answer

$7,7,8\frac{1}{2}$

Exercise #14

The combined size of the angles between two edges of the cuboid is...?

Video Solution

Answer

$90$

Exercise #15

Look at the orthohedron in the figure below.

Which angle is between the diagonal BH and the face ABFE?

Video Solution

Answer

$HBE$

Question 1

What is the longest segment of the rectangular prism in the diagram?

Question 2

What does the angle in the figure represent?

Question 3

The orthohedron in the figure is square (the shaded sides are equal).

How many diagonals like the dotted diagonal in the diagram are there in the orthohedron?

Exercise #16

What is the longest segment of the rectangular prism in the diagram?

Video Solution

Answer

$AG$

Exercise #17

What does the angle in the figure represent?

Video Solution

Answer

The angle between the diagonal of the rectangular prism and its base.

Exercise #18

The orthohedron in the figure is square (the shaded sides are equal).

How many diagonals like the dotted diagonal in the diagram are there in the orthohedron?

Video Solution

Answer

$8$