Similar figures: length, area and volume
When a figure is enlarged by scale factor k, lengths grow k times, areas k squared times and volumes k cubed times. Use a ratio table to find the missing size.
- إيران: الصف ٩
- أفغانستان: الصف ٨
- روسيا: الصف ٨
- ألمانيا: الصف ٩
- فرنسا: الصف ٩
- بريطانيا: السنة ١٠
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
Two figures are متشابه when one is an enlargement of the other. The نسبة التشابه k tells you how many times every length grows.
An المساحة is length times length, so it grows by k × k = k٢. A الحجم is length times length times length, so it grows by k٣.
Example: enlarge a square of side 2 cm by k = 3. The side becomes 6 cm, the area goes from 4 cm² to 36 cm² (4 × 9), and a cube of that side would go from 8 cm³ to 216 cm³ (8 × 27).
Working backwards: if the areas are in the ratio 9 : 1, then k٢ = ٩, so k = 3. Take the square root to get back to lengths from areas, and the cube root from volumes.
In the ratio table each row is one size of the figure. Fill in the missing cell.