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3D Shapes Practice Questions

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Course: 6th grade   >   Unit 10

• Counting faces and edges of 3D shapes
• Identify parts of 3D shapes

Recognizing common 3D shapes

• Identify geometric solids (3D shapes)

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Video transcript

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The Shape Shed

Shapes and more shapes

2D Shape Draw.

3d shape properties., mr men and little miss 2d shape mat., minecraft mega shape challenge., superhero shape pictures., how many shapes, 3d shape addition., explain everything app and shape properties., lego symmetry.

• Basic level: build a Lego creation with at least one line of symmetry. When you're done, show the lines of symmetry.
• Advanced: decide on how many lines of symmetry the creation will have. One? Two? More? Build a structure to those specifications.
• Basic: build a Lego creation with rotational symmetry. You choose the order of rotation.
• Advanced: decide on an order of rotation and build a project to match.

Our Lego Wall Project from Tricia Fuglestad on Vimeo .

3D Shape Mat.

Dr who and the flatliners : 3d shape, 3d shape posters., shape song swingalong., circle song., polygon song., parallelogram song. , quadrilaterals., symmetry everywhere, angry birds - an introduction to 2d and 3d shape..

Applying Pythagoras' theorem Using Pythagoras in 3D

Pythagoras' theorem states that for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Part of Maths Geometric skills

Using Pythagoras in 3D

Pythagoras' theorem can also be used to solve 3D problems. You often need to use Pythagoras' theorem more than once in each problem as we create extra right-angled triangles in the 3D shapes.

This cuboid has side lengths of 2cm, 3cm and 6cm.

Work out the length of the diagonal AF.

First use Pythagoras' theorem in triangle ABC to find length AC.

\(A{C^2} = {6^2} + {2^2}\) (as BC must be 2cm)

\(AC = \sqrt {40}\)

You do not need to find the root as we will need to square it in the following step. Next we use Pythagoras' theorem in triangle ACF to find length AF.

\(A{F^2} = A{C^2} + C{F^2}\)

\(AF^{2}=(\sqrt{40})^{2}+3^{2}\)

\(AF^{2}= 40+9\)

\(AF^{2}=49\)

\(AF = \sqrt {49}\)

\(AF = 7cm\)

Now try the example question below.

Work out the vertical height (VM) in this square-based pyramid and give your answer to one decimal place.

The square base ABCD has side lengths of 5cm.

Lengths VA, VB, VC and VD are each 8cm.

M is the mid point of the square base.

Show answer Hide answer

First find the diagonal length of the base AC to 1 decimal place.

\(A{C^2} = A{B^2} + A{D^2}\)

\(A{C^2} = {5^2} + {5^2}\)

\(A{C^2} = 25 + 25 = 50\)

\(AC = \sqrt {50}\)

\(AC = 7.07\)

To find AM, we need \(\frac{1}{2}\) of AC.

\(AM = \frac{1}{2} \times AC\)

\(AM = \frac{1}{2} \times 7.07\)

\(AM=3.54\)

Now that we know two dimensions of the triangle VMA inside our pyramid, we can calculate the length of VM.

\(V{M^2} = V{A^2} - A{M^2}\)

\(V{M^2} = {8^2} - {3.54^2}\)

\(V{M^2} = 64 - 12.53\)

\(V{M^2} = 51.47\)

\(VM = \sqrt {51.47}\)

\(VM = 7.2cm\) (to 1 decimal place)

• Remember to use at least one more decimal place than you are asked for during your calculation.
• When giving your final answer, always round according to what the question is asking for, in this case one decimal place.

More guides on this topic

• Determine the gradient of a straight line
• Circle geometry
• Calculating the volume of a standard solid
• Applying the properties of shapes to determine an angle
• Using similarity
• Working with two-dimensional vectors
• Working with three-dimensional coordinates
• Using vector components
• Calculating the magnitude of a vector
• An Approximate History of Co-ordinates

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Deepen understanding of 3-D shapes - Problem-Solving Investigation - Year 5

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

15 April 2024

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This in-depth maths investigation is an open-ended problem solving activity for Year 5 children. It can be used to support teaching towards the objectives: Revise and deepen understanding of properties of 3-D shapes.

In-depth investigation: Pharaoh’s Rest By looking at this net for a square-based pyramid, can you visualise and draw other, different nets that fold to give the same pyramid?

This investigation will develop maths meta-skills, support open-ended questioning and logical reasoning, and enable children to learn to think mathematically and articulate mathematical ideas. This problem-solving investigation is part of our Year 5 Shape block. Each Hamilton maths block contains a complete set of planning and resources to teach a term’s worth of objectives for one of the National Curriculum for England’s maths areas.

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Resources tagged with: Nets

There are 23 NRICH Mathematical resources connected to Nets , you may find related items under 3D geometry, shape and space .

The Spider and the Fly

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

A Puzzling Cube

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Tet-trouble

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

Which Face?

Which faces are opposite each other when this net is folded into a cube?

Cool as Ice

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Make Your Own Pencil Case

What shape would fit your pens and pencils best? How can you make it?

Chopped Dice

Can you make a new type of fair die with 14 faces by shaving the corners off a cube?

Auditorium Steps

What is the shape of wrapping paper that you would need to completely wrap this model?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Triangular Faces

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

All Wrapped Up

What is the largest cuboid you can wrap in an A3 sheet of paper?

All Is Number

Read all about Pythagoras' mathematical discoveries in this article written for students.

Thinking 3D

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?

More Christmas Boxes

What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?

Cubic Conundrum

Which of the following cubes can be made from these nets?

Cutting a Cube

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Rhombicubocts

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

Let's Face It

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Face Painting

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Platonic Planet

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?