The horizontal cross-sections of a cone are circular in shape, and these circles are congruent to each other at all heights except for the vertex, which is a single point. As you move away from the vertex along the height of the cone, the diameter of the circular cross-sections increases uniformly. This consistent shape results in a series of congruent circles, illustrating the cone's geometric properties.
True
True
true!!
True
False. Every cross-sectional shape of a cone is not congruent.
The horizontal cross-sections of a cone are circular in shape, and these circles are congruent to each other at all heights except for the vertex, which is a single point. As you move away from the vertex along the height of the cone, the diameter of the circular cross-sections increases uniformly. This consistent shape results in a series of congruent circles, illustrating the cone's geometric properties.
In a standard cylinder, all horizontal cross-sections are congruent circles regardless of the height at which the cut is made. If the statement asserts that the cross-sections are not all congruent, it suggests that the figure in question may not be a true cylinder. Instead, it could be a shape that varies in diameter along its height, such as a tapered or irregular prism.
false
True
True
true!!
True
A solid that has congruent horizontal and vertical cross sections is a cylinder. In a cylinder, both the horizontal cross sections (circles) and vertical cross sections (rectangles) maintain consistent dimensions throughout the solid. This property ensures that the shapes formed by slicing the cylinder in any horizontal or vertical plane are always congruent to each other. Other examples include cubes and spheres, but the cylinder specifically illustrates this characteristic well.
true!!
true!!
No because it would be smaller.