GCSE · Maths · OCR · Spec J560

Plans and elevations

A flat triangle on a page can be a cone's front view and its side view at once. Sort a few drawings and watch views overlap.

Which view is it?

Sort the drawings into their views

A plan is what you see looking down from above. A front elevation is what you see from the front. A side elevation is what you see from the side. Each drawing below is one view of a solid. Tick every view it could be. The cuboid is 6 cm long, 4 cm deep and 3 cm tall, and you face one of its 6 cm sides.

  • A Plan (from above)
  • B Front elevation (from the front)
  • C Side elevation (from the side)
  1. Cuboid: a rectangle 6 cm by 4 cm
  2. Cuboid: a rectangle 6 cm by 3 cm
  3. Cuboid: a rectangle 4 cm by 3 cm
  4. Cone: a circle with a point at its centre
  5. Cone: a triangle whose base is double the radius
  6. Cylinder: a circle
  7. Cylinder: a rectangle
  8. Cube: a square

Exam line: Name a view from its shape and its lengths, and remember that one drawing can be more than one view.

Draw the three views of a cube-built solid

Problem

A solid is built from three 1 cm cubes, drawn on isometric paper: two cubes side by side at the front, and a third cube directly behind the left-hand one. Draw its plan, front elevation and side elevation, looking at the side from the right, on squared paper with 1 cm per square.

Now run it backwards

You have the views. What solid made them?

A solid has a circle as its plan. Its front elevation and side elevation are both rectangles 4 cm wide and 6 cm tall. Which sketch on isometric paper matches all three views?

Same views, different solids?

Solid A: a plain cuboidvsSolid B: the same cuboid with a hollow sealed inside it

Two solids, three identical drawings. Where could they possibly differ?

Focus

Plan

Solid A: a plain cuboid

A rectangle 5 cm by 3 cm

Solid B: the same cuboid with a hollow sealed inside it

A rectangle 5 cm by 3 cm

The insight

The plan only shows what you see from above, so it can't tell them apart.

Front elevation

Solid A: a plain cuboid

A rectangle 5 cm by 2 cm

Solid B: the same cuboid with a hollow sealed inside it

A rectangle 5 cm by 2 cm

Side elevation

Solid A: a plain cuboid

A rectangle 3 cm by 2 cm

Solid B: the same cuboid with a hollow sealed inside it

A rectangle 3 cm by 2 cm

Features inside

Solid A: a plain cuboid

Nothing: solid all the way through

Solid B: the same cuboid with a hollow sealed inside it

A hollow space inside

Which idea is closest to yours?

How long is a sloped face?

A solid has a sloped rectangular face. In its side elevation, that face is drawn 3 cm high.

What do you think the real length of the sloped face is?
How sure are you?

Exam line: A length in an elevation is not always a true edge length.

Have a go, then mark yourself

Shrink a shed to scale

A shed is 3 m wide. A designer draws its plan and its front elevation at a scale of 1:20, and the 3 m width appears in both drawings. Work out the width of the shed on the plan, in cm, showing how you convert the units. Then say what width the front elevation must show for the same edge, and why. [4 marks]

0 words · your answer stays on this page and is not sent anywhere.

Exam line: Convert to the same unit first, then divide by the scale. Then use the drawings to check corresponding lengths.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Look from above, from the front and from the side, then work backwards from the drawings to the solid.

What you need to know

  • The plan is the view of a solid from above.
  • Looking from the front gives the front elevation; looking from the side gives the side elevation.
  • Have a goYour friend says, 'Looking down on a solid from above gives you its front elevation, because it's the front of the top.' Which view is it really?

    The plan.

    The direction you look from decides the name: from above is the plan, from the front is the front elevation.

  • Each viewpoint shows a different face, so the shapes you see and their lengths tell you which view it is.
  • Have a goTwo drawings of the same cuboid are both rectangles. What else do you check to tell which view each one is?

    Their lengths.

    A shape such as a rectangle can turn up in more than one view, so the shape alone doesn't settle it; the lengths help.

  • A cone's plan is a circle whose centre point marks the tip; its front and side elevations are the same triangle.
  • That triangle's base is double the cone's radius.
  • Have a goA cone has a radius of 5 cm. How wide is the base of the triangle in its front elevation?

    10 cm.

    The base of the triangle is double the radius, not the radius itself.

  • A solid with a circle for its plan and congruent rectangles for its front and side elevations is a cylinder.
  • Where faces meet at a break rather than forming one continuous face, you draw that break on the view.
  • Sloped faces appear shorter in an elevation than their actual length.
  • To sketch a solid you need all three views, yet different solids can share the same plan, front elevation and side elevation.
  • On a scale drawing, a ratio such as 1:50 means 1 cm on the drawing represents 50 cm in real life.

The big picture

A plan, a front elevation and a side elevation are three viewpoints on the same solid: from above, from the front and from the side. You can name a view from its shapes and lengths, build a solid back from its views, and use scale to solve problems. Views can overlap, they can hide what is inside, and they can show a sloped face shorter than it really is.

Key points

1The plan is the view from above, the front elevation is the view from the front, and the side elevation is the view from the side.
2Each view is a viewpoint: you identify it by the shapes seen and their lengths, and one drawing can be more than one view of the same solid.
3Plans and elevations do not show features inside a solid, so more than one solid can share the same three views.
4A sloped face appears shorter in an elevation than its actual length.

Worked example

Problem

A plan of a hall is drawn at a scale of 1:25. A wall measures 8 cm on the drawing. What is the real length of the wall, in metres?

⚠ Watch out

Treating a drawn length as the true edge length. On a sloped face, the elevation shows the face shorter than it really is.

🧠

Memory hook

Plan sounds like plane: picture a plane flying over, looking down. Elevations are what you see by standing in front or to the side.

✓

Check yourself

Cover the page and explain to a friend why a cone's single triangle counts as two views, and why three views of a solid might still not tell you what is inside it.

Flashcards

(15)
Plan, front elevation, side elevation: which direction is each viewed from?
Plan: from above. Front elevation: from the front. Side elevation: from the side.
How can you identify which view a drawing is?
By the shapes seen and their lengths. Each point of view shows a different face.
In a cuboid, what do you know about edges that are parallel to each other?
They are the same length.
What is the plan of a cone?
A circle. Its centre point marks the tip of the cone.
What are the front and side elevations of a cone?
The same triangle, whose base is double the radius.
Which curved solid has a circle for its plan and congruent rectangles for its front and side elevations?
A cylinder.
In a view of a cube-built solid, when do you draw a break?
Where faces at different depths meet and are not one continuous face.
Why do squared-paper views not look exactly like the solid on isometric paper?
The grid lines on the two types of paper are not the same. The measurements for each line have not changed.
Do the plan and elevations show everything about a solid?
No. They do not show features inside it, and multiple solids can have the same three views, so more information may be needed.
How does a sloped face appear in an elevation?
Shorter than its actual length.
What does a scale of 1:50 mean?
1 cm on the drawing represents 50 cm in real life. For example, 7 m = 700 cm is drawn as 14 cm.
What do you need in order to sketch a solid from its views, and what should the sketch be like?
All three: the plan, front elevation and side elevation. The sketch should be clear, relatively in proportion, with relevant edges parallel and lengths shown.
Is it possible to draw a curve on isometric paper?
Yes.
How do you draw a view on plain paper?
Label the known lengths, and use a ruler to draw right angles and lines accurately.
How can an isometric drawing help with plans and elevations?
Combine it with the plan and elevations to find missing information, or check that corresponding lengths are equal between the drawings.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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