1. Volume is a measure of the amount of space that an object occupies in three-dimensional space.
2. The volume of a cylinder and a cone with the same height and radius are related in that the volume of the cone is precisely one-third of that of the cylinder.
3. The volume of a cylinder and a sphere cannot be directly compared. They have different formulas for finding their volume and the shapes are different. However, it is interesting to note that the volume of a sphere is 4/3 times the volume of a circumscribed cylinder.
4. The volume of a prism and a pyramid with the same base and height are related in that the volume of the pyramid is precisely one-third of that of the prism.
5. The volume of a prism and a cylinder with the same base and height are related in that the volume of the cylinder is precisely equal to the volume of the prism multiplied by the factor of pi/4. This means that the volume of a cylinder is greater than the volume of a prism of the same base and height.
Answers & Comments
Answer:
1. Volume is a measure of the amount of space that an object occupies in three-dimensional space.
2. The volume of a cylinder and a cone with the same height and radius are related in that the volume of the cone is precisely one-third of that of the cylinder.
3. The volume of a cylinder and a sphere cannot be directly compared. They have different formulas for finding their volume and the shapes are different. However, it is interesting to note that the volume of a sphere is 4/3 times the volume of a circumscribed cylinder.
4. The volume of a prism and a pyramid with the same base and height are related in that the volume of the pyramid is precisely one-third of that of the prism.
5. The volume of a prism and a cylinder with the same base and height are related in that the volume of the cylinder is precisely equal to the volume of the prism multiplied by the factor of pi/4. This means that the volume of a cylinder is greater than the volume of a prism of the same base and height.