Question

Which shapes could be formed when a 2-dimensional plane cuts the cylinder?

Answer 1

When a 2-dimensional plane cuts a cylinder, different shapes can be formed depending on the angle and position of the cut.

Step-by-step explanation:

When a 2-dimensional plane cuts a cylinder, different shapes can be formed depending on the angle and position of the cut. Here are some examples:

• If the plane cuts the cylinder parallel to its bases, the resulting shape is a rectangle or square, depending on the dimensions of the cylinder.
• If the plane cuts the cylinder at an angle, the resulting shape is an ellipse or an oval.
• If the plane cuts through the curved surface of the cylinder diagonally, the resulting shape is a curved section called an ellipse.
• If the plane cuts through the cylinder at an angle that is perpendicular to the base, the resulting shape is a triangle.

Answer 2

When a 2-dimensional plane cuts through a cylinder, various shapes can be formed, including a circle, ellipse, parabola, hyperbola, line, and point. The specific shape depends on the angle and position of the plane.

When a 2-dimensional plane cuts through a cylinder, several different shapes can be formed. Some of the possible shapes include a circle, an ellipse, a parabola, a hyperbola, a line, and a point. Which shape is formed depends on the angle and position at which the plane intersects the cylinder.

For example, if the plane is perpendicular to the axis of the cylinder, a circle will be formed. If the plane cuts through the cylinder at an angle, an ellipse will be formed. If the plane cuts through only one side of the cylinder, a parabola or a hyperbola may be formed. And if the plane intersects the cylinder at a single point, a point or a line may be formed.

The specific shape that is formed can be determined using mathematical principles and equations related to conic sections, such as the equation of the plane and the equation of the cylinder.