What is the volume of the solid produced?
A hard-level "Volume" problem.A solid of revolution is just cylinders added step by step. The radius is always the distance from the axis — never a vertical measurement of the shape.
GivenThe L-shape is spun once around the dotted axis / π = 3.14
Hints
- A solid of revolution is hard to take in all at once. Cut it at the step: the shape becomes two rectangles, a blue one below and a green one above.
- Spinning a rectangle around the axis makes a cylinder. Its radius is the farthest distance from the axis, here 5 cm. So the lower part is 5 × 5 × 3.14 × 3 = 235.5 cm³.
- The upper part works the same way, but reaches only 3 cm from the axis, so it makes a slimmer cylinder: 3 × 3 × 3.14 × 3 = 84.78 cm³.
- Add the two cylinders: 235.5 + 84.78 = 320.28 cm³. However many steps there are, the same slicing works.
Answer 320.28cm³
More "Volume" problems
- What is the volume of the bottom part?
- Volume of the solid made by one full turn?
- Volume of the stone?
- Volume of the cuboid?
- What is the volume of the box?
- Volume of the cylinder?