What is the volume of the bottom part?
A hard-level "Volume" problem.Double the lengths and areas quadruple, volumes go up eightfold. Not mixing up the square and the cube is the whole game in similarity problems.
GivenA cone is cut parallel to its base, exactly halfway up. The small cone on top has volume 9 cm³.
Hints
- Because the cut is parallel to the base, the small top cone is just the whole cone shrunk — they are similar. That is the starting point.
- The height was divided by 2, so the base radius is divided by 2 too. Every length is scaled the same way.
- Here is the key. If lengths are multiplied by 2, areas go up by 2×2 = 4. Volume grows in all three directions, so it is multiplied by 2×2×2 = 8.
- So the whole original cone is 8 times the small one: 9 × 8 = 72 cm³.
- The question asks for the bottom part, so subtract the top from the whole: 72 − 9 = 63 cm³.
Answer 63cm³
More "Volume" problems
- Volume of the solid made by one full turn?
- What is the volume of the solid produced?
- Volume of the stone?
- Volume of the cuboid?
- What is the volume of the box?
- Volume of the cylinder?