GCSE · Geometry and measures

Plans and elevations

Build a solid from cube stacks and compare its top, front and right-side views.

Change the back row of stacks without exceeding the front heights. Compare the front view before and after.

V=number of unit cubesV=\text{number of unit cubes}
Plans and elevationsFrontRight sideFront: y = 0 · Right side: x = 3

Scroll the diagram sideways to see every label.

Plan (top)1221113Front elevationRight elevation

Plan numbers are stack heights to help you check; an ordinary plan shows only the occupied squares. Right-view columns run from front to back.

11 cubes; 7 occupied squares in the plan.

Volume
11 cubic units
Exposed area
42 square units
Front heights
2, 2, 3
Right heights
2, 2, 3

Each stack stands on the ground. Area counts every exposed unit face, including the underside. Views are orthographic: depth is collapsed, not drawn in perspective.

Predict, test and explain

Step 1 of 3

Predict

Does a front elevation show every cube?

InvestigateChange the back row of stacks without exceeding the front heights. Compare the front view before and after.

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

Notes and saved values stay in this tab. They disappear when you reload.

Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Does a front elevation show every cube?

Hint

An elevation records the greatest height along each sight line; it does not count hidden cubes.

Reveal answer

An elevation records the greatest height along each sight line; it does not count hidden cubes.

Build an explanation

Hint 1

An elevation records the greatest height along each sight line; it does not count hidden cubes.

Hint 2

Use the labels and units in the live model to check your method.

Hint 3

Explain which lengths, areas or volumes are being compared.

Worked example

This example uses fixed values, separate from the diagram controls.

For a 2 by 2 footprint, front-row heights are 1, 3 and back-row heights are 2, 1. Find the front elevation heights and total cubes.

  1. Look along the depth for each column.
  2. Take max(1, 2) and max(3, 1) to get the front heights.
  3. Add all stack heights to count cubes: 1 + 3 + 2 + 1.

Answer: Front heights 2, 3; 7 cubes.

Connect this idea

Watch out: An elevation records the greatest height along each sight line; it does not count hidden cubes.