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Year 4 Maths 3D Objects

Draw & interpret views of 3D objects

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Theory

Drawing and interpreting views of 3D objects is a Year 4 maths space skill: a view is the flat 2D shape you see when you look at a solid from one direction. This page explains the front, top and side views of everyday solids like cubes, cylinders and cones, and how to count the squares in the views of a stack of cubes. Curriculum: taught in Year 4 in Western Australia. The Australian Curriculum and the Victorian Curriculum have no separate Year 3 to 6 content description for views of 3D objects; the nearest content, nets of 3D objects, is in Year 5 (AC9M5SP01 / VC2M5SP01).

A view of a 3D object is the flat 2D shape you see when you look at it from one direction. The same solid looks different from different sides, so we draw more than one view to describe it.

The three main views are the front view (looking straight at the front), the top view or plan view (looking straight down from above), and the side view (looking straight at one end). Each view is a flat outline, not a picture of the whole solid.

When a solid is built from cubes, each view is a flat grid of squares. You count the squares along and up. Some cubes may be hidden behind others, so a view does not always tell you how many cubes there are.

An L-shaped stack of five cubes A stack of cubes: a bottom row of four cubes with one more cube resting on top of the left cube.
A stack of cubes seen as a 3D object.
Front, top and side views of the cube stack Three flat grids of squares. The front view is an L of five squares, the top view is a row of four squares, and the side view is a column of two squares. FrontTopSide
Its front view (an L of 5 squares), top view (a row of 4 squares) and side view (2 squares).

Views do not need a formula, but these facts help you name the views quickly. This table gives the front, top and side views of some common solids.

ObjectFront viewTop viewSide view
Cubesquaresquaresquare
Rectangular prism (box)rectanglerectanglerectangle
Cylinder (standing up)rectanglecirclerectangle
Cone (point up)trianglecircle with a dot in the centretriangle
Sphere (ball)circlecirclecircle
Square pyramidtrianglesquaretriangle

For a full stack of cubes, the number of squares in the front view is the length times the height:

\[ \text{front-view squares} = \text{length} \times \text{height} \]
front-view squares=length×height
One view is not enough. A circle from the top could be a can, a ball or a cone. Look from the front as well to tell them apart, because each one has a different front view.

For a full stack with no gaps, you can count every cube, the hidden ones too:

\[ \text{number of cubes} = \text{front-view squares} \times \text{depth} \]
number of cubes = front-view squares × depth

How to draw a view of a 3D object

  1. Choose the direction. Decide if you are looking from the front, from the top or from the side.
  2. Look for the flat outline. Imagine the shape squashed flat against a wall. Round edges that face you look straight.
  3. Draw it flat. For a stack of cubes, draw a grid of squares. Count the squares along, then up, and ignore the cubes hidden behind.
  4. Top view of a stack. Looking down, a cube on top hides the cube under it, so count one square for each place where cubes stand.
  5. Counting all the cubes. For a full stack with no gaps, multiply the front-view squares by the number of cubes from front to back. Remember the hidden cubes.
Example 1 — Views of a tent
A tent is shaped like a triangular prism lying on one of its rectangle faces, with a triangle end at the front. What are its front view and top view?
A tent with its front view and top view A tent shaped like a triangular prism lying on a rectangle face, with a triangle end at the front. Its front view is a triangle and its top view is a rectangle with a line along the middle for the ridge. The tent Front view Top view
Solution
\(\text{front view}\)\(=\)\(\text{triangle}\)
\(\text{top view}\)\(=\)\(\text{rectangle}\)

From the front you see the triangle end. Looking down, you see the two sloping sides next to each other, which make a rectangle with a line along the ridge.

Example 2 — Front and top views
This stack has a bottom row of 3 cubes, with 2 more cubes stacked on the right-hand cube.
(i) How many squares are in the front view?
(ii) How many squares are in the top view?
A stack of five cubes A stack of cubes: a bottom row of three cubes, with two more cubes stacked on top of the right-hand cube.
Solution
\(\text{front}\)\(=\)\(3 + 2 = 5\)
\(\text{top}\)\(=\)\(3\)

(i) \(5\) squares. (ii) \(3\) squares, because from above each cube on top hides the cube under it.

Example 3 — Three views and all the cubes
This full box of cubes is 4 long, 2 deep and 2 high, with no gaps.
(i) How many squares are in the front, top and side views?
(ii) How many cubes are there altogether?
A full box of cubes four long, two deep and two high A solid box built from cubes, four cubes long, two cubes deep and two cubes high, packed full with no gaps.
Solution
\(\text{front}\)\(=\)\(4 \times 2 = 8\)
\(\text{top}\)\(=\)\(4 \times 2 = 8\)
\(\text{side}\)\(=\)\(2 \times 2 = 4\)
\(\text{all cubes}\)\(=\)\(8 \times 2 = 16\)

(i) Front \(8\), top \(8\), side \(4\) squares. (ii) \(16\) cubes, including the \(8\) hidden at the back.

Example 4 — Same view, hidden cubes
One stack is a wall 5 cubes long and 2 cubes high, 1 cube deep. Another is the same wall but 2 cubes deep.
(i) Do they look the same from the front?
(ii) How many cubes does each stack have?
Solution
\(\text{wall } 1\text{ deep}\)\(=\)\(5 \times 2 = 10\text{ cubes}\)
\(\text{wall } 2\text{ deep}\)\(=\)\(10 \times 2 = 20\text{ cubes}\)

(i) Yes. Both show the same \(10\) squares from the front; the extra cubes are hidden behind. (ii) \(10\) cubes and \(20\) cubes.

Common pitfalls

A view is flat. Watch out for drawing a 3D box with slanted sides. A view is a flat 2D outline of squares or simple shapes.
Count squares, not cubes. The front view of a full stack shows only the front squares. The cubes hidden behind do not add to the view.
Match the direction to the view. The top view is what you see looking down, so it shows length and width, never height. Do not mix it up with the front view.

Frequently asked questions

What is the front view of an object?

The front view is the flat 2D shape you see when you look straight at the front of the object. It shows the length and the height.

What is the top view of an object?

The top view, also called the plan view, is what you see when you look straight down on the object from above. It shows the length and the width, not the height.

How do you find the views of a stack of cubes?

Look at the stack from each direction and draw the outline as flat squares. Count the squares along and up to find the front, top and side views.

Can two different solids have the same view?

Yes. Cubes hidden behind others do not change the front view, so a wall one cube deep and the same wall two cubes deep look exactly the same from the front.

What is the side view of an object?

The side view is the flat shape you see when you look straight at one end of the object. It shows how deep the object is and how high it is.

What is the difference between a top view and a front view?

The top view is seen looking down and shows length and width. The front view is seen looking straight ahead and shows length and height.

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