lesson
Each dimension contributes a factor
1 · Learn
An enlargement by length scale factor k multiplies corresponding lengths by k. Areas scale by k² because two dimensions change; volumes scale by k³ because three dimensions change.
Do not apply the length factor unchanged to area or volume. This assumes the shapes or solids are geometrically similar, with all relevant lengths scaled consistently.
2 · Worked example
A similar solid enlarged by factor 2 has twice the lengths, four times the surface area and eight times the volume.
3 · Your turn
Similar rectangles have length scale factor 3. If the smaller area is 12 cm², find the larger area.
Check your answer
12 × 9 = 108 cm².
4 · Apply your learning
Draw a 4 cm by 3 cm rectangle on squared paper. Enlarge both lengths by scale factor 3 to 12 cm and 9 cm. Count or calculate the areas and explain why 12 cm² becomes 108 cm², not 36 cm².
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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