Similar figures
A standard method from Arcs, sectors and mensuration: the steps and worked examples.
Steps
If the scale factor of lengths is k:
- area ratio = k²;
- volume ratio = k³.
Worked examples
Example 1: Two similar cylinders have heights 4 cm and 6 cm. The smaller one has volume 40 cm³. Find the larger volume.
volume ratio = (4/6)³ = 8 : 27
larger volume = 40 × 27/8 = 135 cm³For the whole topic, read Arcs, sectors and mensuration: key points, common mistakes and how the DSE tests it.