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Some of the classic curves studied by mathematicians: ellipses, hyperbola are cross sections of a cone taken at an angle.
When a sphere is cut with a vertical angled plane, the cross-section will be an ellipse. If the sphere is then cut by a horizontal plane, the cross-section will be a circle. Thus, the combination of these two cuts results in an elliptical cross-section from the angled cut and circular cross-sections from the horizontal cuts at various heights.
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.
If horizontal, a circle. If vertical, a semi-circle.
The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.
It is a rectangle which is similar to the base.
When a sphere is cut with a vertical angled plane, the cross-section will be an ellipse. If the sphere is then cut by a horizontal plane, the cross-section will be a circle. Thus, the combination of these two cuts results in an elliptical cross-section from the angled cut and circular cross-sections from the horizontal cuts at various heights.
They are all circles. The vertical and horizontal have the same radius as the ball while the angled cross section has a smaller radius.
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.
If horizontal, a circle. If vertical, a semi-circle.
The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.
The vertical cross section of a right vertical cone is a triangle if that cross section is taken from the vertex. Any other vertical cross section will reveal a hyperbola (with endpoints on the base of the cone). A link can be found below.
It is a rectangle which is similar to the base.
Jesus was crucified on a cross. The main section was vertical and the cross bar was horizontal and a few feet below the top of the main section as we are told that a sign was placed on the cross above His head. We do not know what kind of wood the cross was made of.
Christian Cross: 1 - Vertical symmetry Maltese Cross: 4 - Vertical, Horizontal and two diagonals
If the cylinder is standing on its flat face, the horizontal cross section is a circle. Otherwise, it is a line or a rectangle.
The vertical cross section of a rectangle is obtained by slicing the rectangle vertically, which results in a shape that retains the same height as the original rectangle but may vary in width depending on where the cut is made. If the cut is made parallel to one of the rectangle's sides, the vertical cross section will be another rectangle. If the cut is made at an angle or through the middle, the resulting shape will depend on the specifics of the cut. Overall, the vertical cross section will always reflect the height of the original rectangle.
Circle