Study guides › Level 7 · Geometry

Scale: what happens to area and volume

Level 7 · Geometry · for questions like “A photo is enlarged so every length is 3 times as long. How many times as big is its area?”

💡 The idea

If every length is multiplied by k:

• area is multiplied by k² (length and width both grow);
• volume is multiplied by k³ (length, width and height all grow).

✏️ Worked examples

1. Lengths × 3: the area is × 9.

2. Lengths × 2: the volume is × 8.

3. A 20 sq in poster, lengths × 4: 20 × 16 = 320 sq in.

⚠️ Watch out

• Area doesn't just double when the lengths double. It's × 4.

🎯 Try these

1. Lengths × 5: area?
2. Lengths × 3: volume?
3. A 15 sq cm picture with lengths × 2: new area?

Answers: 1) × 25 2) × 27 3) 60 sq cm

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