Similarity · Grade 11
In Grade 11 you get fluent with: area and volume in similar shapes.
Similar shapes have the same shape but can be different sizes: their angles are equal and all their lengths are in the same ratio, the scale factor. Areas grow by the square of the scale factor and volumes by its cube.
Key facts
- Area scale factor = k².
- Volume scale factor = k³.
Worked examples
Example 1
Two similar shapes have lengths in the ratio 2 : 5. The smaller has an area of 12 cm². Find the area of the larger.
Answer: 75 cm²
Example 2
Two similar jugs hold 250 ml and 2,000 ml. The small jug is 10 cm tall. How tall is the large jug?
Answer: 20 cm
Example 3
Two similar cylinders have volumes 16 cm³ and 54 cm³. The small one is 4 cm tall. How tall is the large one?
Answer: 6 cm
Example 4
Two similar triangles have areas of 9 cm² and 25 cm². A side of the smaller one is 6 cm. Find the matching side of the larger one.
Answer: 10 cm