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See Plans →A 3D shape can be described completely using three 2D views, each taken from a different direction:
Plan view — looking straight down from above (bird's eye view). It shows the footprint or floor plan of the object.
Front elevation — looking from directly in front. It shows the height and width of the object.
Side elevation — looking from the side. It shows the height and depth of the object.
Together, all three views give enough information to fully reconstruct the 3D shape.
A cuboid is 4 cm wide, 6 cm long and 3 cm tall. Describe each view.
Looking down, you see the length and width: a rectangle \(6\text{ cm} \times 4\text{ cm}\).
Looking from the front, you see the length and height: a rectangle \(6\text{ cm} \times 3\text{ cm}\).
Looking from the side, you see the width and height: a rectangle \(4\text{ cm} \times 3\text{ cm}\).
A step shape consists of two cuboids: a bottom block 6 cm wide × 4 cm deep × 2 cm tall, and a top block 3 cm wide × 4 cm deep × 2 cm tall sitting on top of the left half. What does the front elevation look like?
Stand in front of the shape and look straight at it. You project horizontally inwards.
The base cuboid is 6 cm wide and 2 cm tall — draw a rectangle spanning the full width at the bottom.
The top block is 3 cm wide and 2 cm tall, sitting on the left half. Draw a narrower rectangle on top of the left half of the base.
The front elevation is an L-shape (or stepped rectangle) — taller on the left, shorter on the right.
To draw a view, project lines from the 3D object in the direction of the view and record only what you can see from that direction.
Hidden edges (edges you cannot see directly but which exist) are shown as dashed lines.
On squared or dotted paper, let 1 square = 1 unit. Be precise — measurements must be accurate.
Three unit cubes are arranged in an L shape on a grid (2 in a row, then 1 above the left). Draw and describe the plan, front elevation and side elevation.
Two cubes side by side (left and right), plus one cube on top of the left cube.
Looking down: the two bottom cubes give a 2×1 rectangle. The top cube sits directly above the left cube, so the footprint is still just 2×1 (the top cube doesn't extend the footprint). Plan = a 2 × 1 rectangle.
Looking from the front: the right cube is 1 unit tall. The left cube has another cube on top so is 2 units tall. Front elevation = a stepped L-shape: 2 squares wide at base (1 tall each), left side has extra square on top.
Looking from the right side: you see the right cube (1 unit) in front and the left column (2 units) behind. From the side, you see the tallest part = 2 units tall, 1 unit deep. Side elevation = a 1 × 2 rectangle.
A square pyramid sits on top of a cube of side 4 cm. Draw the plan and front elevation.
From above: the cube base shows a 4 cm × 4 cm square. The pyramid sits on top, and from above you see the apex directly above the centre. Draw the 4×4 square, then add both diagonals (corner to corner) to show the pyramid's edges meeting at the apex.
From the front: the cube gives a 4 cm wide × 4 cm tall rectangle. The pyramid sits on top — from the front it looks like a triangle with base 4 cm and some height \(h\). Draw the rectangle (cube) with a triangle on top (pyramid).
Given a set of 2D views, you can work backwards to reconstruct what the 3D shape looks like. This is exactly what architects and engineers do every day.
Strategy:
1. Plan gives the footprint (the shape from above — the base outline)
2. Elevations give the heights and widths (how tall each part is, how wide it is from each side)
3. Combine all three views to build up the full 3D picture
The plan is an L-shape. The front elevation is a stepped rectangle (two different heights). Describe the 3D shape.
L-shaped plan → the footprint (base) of the shape is L-shaped. Two rectangular sections joined at a corner.
Stepped front elevation → one arm of the L is taller than the other. There are two different heights.
Shape = two cuboids of different heights joined side by side, sharing an L-shaped footprint. Because the height changes across the solid, this is not a prism — a prism must have a constant cross-section throughout.
The side elevation would show a rectangle with the height of the taller part and the total depth of the L.
Plan is a circle. Front elevation is a rectangle. Side elevation is also a rectangle with the same dimensions. What is the shape?
Circular footprint → the base of the shape is circular.
The height and diameter are shown — a rectangle means uniform height across the width.
The shape looks the same from the front and side — symmetric in both directions.
Circular base + rectangular elevations (equal) = a cylinder standing upright.
Enter your answers as numbers or shape names.
| # | Question | Answer | Result |
|---|---|---|---|
| 1 | A cuboid is 4 units long, 3 units wide and 2 units tall. How many unit squares are in the plan (top) view? | ||
| 2 | Using the same cuboid, how many unit squares are in the front elevation? | ||
| 3 | Using the same cuboid, how many unit squares are in the side elevation? | ||
| 4 | What is the total surface area of the cuboid (in square units)? | ||
| 5 | A cube has side length 5 units. How many unit squares are in its plan view? | ||
| 6 | A cube (all sides equal). What shape is the plan (top view)? | ||
| 7 | A cylinder standing upright. What shape is the front elevation? | ||
| 8 | A cone (apex at top). What shape is the front elevation? | ||
| 9 | An L-shaped prism (uniform height). What shape is the plan? | ||
| 10 | A cuboid 8 cm × 3 cm × 5 cm. What shape is the side elevation? |