Know Your Keywords — Math, Advanced
Point 16 — Similar 3-D figures
What do we see?
Similar cones, similar cylinders, or similar prisms.
What do we understand?
- Length — a : b
- Perimeter — a : b
- Surface area — a2 : b2
- Volume — a3 : b3
Tips & traps
Stub errors come especially from prism and pyramid volumes — using or forgetting the 1/3.
If the figures are not similar, the volume ratio depends on the actual sides: with H = 3h and R = 6r, the new volume is 6 × 6 × 3 times the old.
Question 1 of 3
| Cone | Radius | Volume |
|---|---|---|
| A | 5 | 125π |
| B | ? | 1000π |
For two right circular cones, with heights h1, h2 and diameters d1, d2 respectively, the cones are similar if = . The table summarizes the dimensions and volumes of two right circular cones A and B. Find the height of cone B.