3D Objects Guide - astreadearne.org

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3D objects are everywhere!

If you look around, you will see objects that are made from many

different 3D objects.

How many can you identify?


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What does 3D mean?

This line has one dimension (length).

Length

Length

Width

This cube has three dimensions (3D). These are length, width and depth.

Length

Width

Depth

This rectangle has length and width, so it has two dimensions.

3D objects are not ‘flat’ like

triangles, squares and

other 2D shapes.


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Here are some 3D objects that you should know.

Cube Cuboid Sphere Cylinder

PrismPyramidCone

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The properties of a 3D object tell us what it is like. We can count the number of faces, edges and vertices.

Vertex A vertex is a corner point

where two lines meet. The plural of vertex is vertices.

Face The faces are the flat parts of a 3D object. These could be squares,

rectangles or other 2D shapes.Edge The edges are the lines where two or more faces meet.

The dotted lines on this image show the edges that we cannot see from the front.

A cube has six faces and

every face is a square. All of the squares are exactly the same size.

Name Cube

Faces 6

Edges 12

Vertices 8


©Did you know that a cube is a special type of cuboid?

A cuboid has six faces. All of these are rectangles

or squares. All of the angles are right angles.


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Name Cuboid

Faces 6

Edges 12

Vertices 8

Boxes are often cuboids. How many cuboids do you see each day?

A sphere is completely

round, like a ball.

Name Sphere

Faces0

(+1 curved surface)

Edges 0

Vertices 0


©Half of a sphere is called a hemi-sphere.

A cylinder has one curved surface and two flat faces at the ends.

Name Cylinder

Faces2

(+1 curved surface)

Edges 2 (curved)

Vertices 0


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The faces at the ends of a cylinder can be

circles or ellipses.

A cone has a flat circular base. The top is pointed and the other

surface is curved.

Name Cone

Faces1

(+1 curved surface)

Edges 1 (curved)

Vertices 0


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The pointed part of a cone is

called the apex.

The base of a cone may be a circle or an ellipse.

A pyramid has a flat base with triangles that

meet to make a point at the top.

Name Pyramid

Faces 5

Edges 8

Vertices 5


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The base of a pyramid can be any shape with straight sides, including a triangle, square, rectangle, hexagon or octagon!

This pyramid has a square base. Other pyramids will have different properties.

Apex

Pyramids are named after the shape

of the base. Here are some examples:

Triangular Pyramid


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Square Pyramid

Pentagonal Pyramid

How many other kinds of pyramid can you think of?

Pyramids can have other

properties too…

Right Pyramid


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Oblique Pyramid

If the apex is directly above the centre of the base,

the object is a right pyramid. If not, it is an

oblique pyramid.

Regular Pyramid Irregular Pyramid

If the base is a regular polygon, the object

is a regular pyramid. If not, it is an irregular

pyramid.

The two ends of a prism are parallel and they are the same size and shape. A prism is also the same

size and shape all the way through.

Name Prism

Faces 7

Edges 15

Vertices 10


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Cubes and cuboids are prisms too! The faces of a

prism are always flat, so a cylinder

is NOT a prism.

The ends of this prism are pentagons.

Other prisms will have different properties.

Prisms are named after the shape that you can

see at the two ends. Here are some examples:


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Triangular Prism Hexagonal Prism

Pentagonal Prism Octagonal Prism

If you cut straight across a prism, the cross-section is always the same shape as the ends.

A polyhedron is a 3D object with many faces.

The plural of polyhedron is polyhedra.


©If the faces are all equilateral triangles, the object is a deltahedra.

Regular Tetrahedron

Regular Octahedron

Regular Hexahedron

Regular Dodecahedron

Regular Icosahedron

If the faces are all the same size and shape, the polyhedron is regular. If not, it is irregular.

A net is a flat shape that can be folded up to make a 3D object.


©Sometimes, different nets can make the same object!

Here are a few examples.

A plane of symmetry cuts a 3D object into two parts

(which are mirror images of each other).


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A single 3D object can have many planes of symmetry.

A plane is like a flat piece of paper or mirror that cuts through the whole object.

The volume of an object is the amount of space that it takes up.

This cube is 1cm long, 1cm wide and 1cm high. Its volume is 1cm x 1cm x 1cm = 1cm3.


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This cuboid is 2cm long, 2cm wide and 1cm high. Its volume is 2cm x 2cm x 1cm = 4cm3.

This cube is 2cm long, 2cm wide and 2cm high. Its volume is 2cm x 2cm x 2cm = 8cm3.

Did you notice the small 3 in the answers? That means ‘cubed’.

The volume of an object is the amount of space that it takes up.

This cuboid is 5cm long, 2cm wide and 3cm high. Its volume is 5cm x 2cm x 3cm = 30cm3.


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5cm

3cm

2cm

To calculate the volume of a cube or cuboid, calculate: Length x Width x Height

Make sure that the measurements of the object are in the same units. Don’t forget to write the 3 (cubed) in your answer!

The surface area of an object is the total area

of all of the faces.

This cuboid is 5cm long, 2cm wide and 3cm high.


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5cm

3cm

2cm

The total surface area is 10cm2 + 10cm2 + 15cm2 + 15cm2 + 6cm2 + 6cm2 = 62cm2.

To calculate the total surface area of a 3D object, work out the area of all of the faces and add them together.

Face Measurements Area

Top 5cm x 2cm 10cm2

Base 5cm x 2cm 10cm2

Front 5cm x 3cm 15cm2

Back 5cm x 3cm 15cm2

Left Face 3cm x 2cm 6cm2

Right Face 3cm x 2cm 6cm2


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Length

Surface Area To find the surface area, work out the area of ALL of the

faces and calculate the total.

A

Volume Area of

cross-section x Length


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Height

Surface Area The area of the base + the area

of all of the other faces.

Volume x Base Area1

3x Perpendicular

Height


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Length

Surface Area 2πr2 + 2πrL

or

2πr(r+L)

Volume πr2 x Length

r


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r

Surface Area πrL + πr2

Volume

hL

L = the slant height

1 3

Type to enter text

πr2h


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Surface Area

4πr2

Volume

4 3 πr3

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3D Objects Guide - astreadearne.org