Lundy’s Rotations And Cross-sections Test

The cross-section of a triangular pyramid perpendicular to its base would be a triangle. This is because when a plane intersects a pyramid perpendicularly to its base, the resulting shape is a cross-section that is similar to the base of the pyramid. Since the base of a triangular pyramid is a triangle, the cross-section would also be a triangle.

The cross-section parallel to the base of a cube would be a square. This is because a cube has equal sides and angles, and when a plane is passed parallel to the base of the cube, it will intersect all four sides of the cube at equal distances, resulting in a square shape.

The perpendicular cross-section of a sphere would give you a circle. A cross-section is a shape that is obtained by cutting through an object in a specific direction. In the case of a sphere, if you were to cut it perpendicular to its axis, the resulting cross-section would be a circle. This is because a sphere is a three-dimensional shape that is perfectly symmetrical in all directions, so any cut made through it would result in a circular shape.

When a penny is spun in space, it would create a spherical shape. This is because in the absence of gravity and air resistance, the penny would continue spinning indefinitely, causing the material to distribute evenly around the center, forming a sphere.

When a triangle is spun in space on its axis, it creates a three-dimensional solid called a cone. A cone is a geometric shape with a circular base and a pointed top, resembling an ice cream cone. The spinning motion of the triangle forms the curved surface of the cone.

If you move a circle parallel in space, you would get a 3D solid known as a cylinder. A cylinder is formed by a circular base and a curved surface that connects the edges of the base. It has two parallel circular faces and a curved surface that wraps around the sides.

When a square is rotated in space, it creates a 3D solid called a cylinder. A cylinder is formed by taking a rectangle and rotating it around one of its sides. The resulting shape has a circular base and a curved surface connecting the two bases. Therefore, a cylinder is the correct answer in this case.

The perpendicular cross-section of a cylinder would make a rectangle. This is because when a cylinder is cut perpendicular to its central axis, the resulting shape is a rectangle. The length of the rectangle corresponds to the height of the cylinder, while the width of the rectangle corresponds to the diameter of the cylinder. Therefore, a rectangle is the correct answer.

If you were to do a parallel cross-section of a square pyramid, the resulting shape would be a square. A parallel cross-section is a cut made parallel to the base of the pyramid, which means it would intersect all the sides of the pyramid at the same distance from the base. Since the base of a square pyramid is a square, the cross-section would also be a square.

A cube is a three-dimensional shape that has six square faces. When a cube is sliced diagonally, one of the resulting cross-sections will be a trapezoid. This is because the diagonally cut section will have two parallel sides of different lengths, which is a defining characteristic of a trapezoid.