Question

1. state whether the following have a circular or rectangular cross section? square pyramid rectangular prism cone cylinder triangular prism cube

Explanation:

Step1: Analyze Square Pyramid

A square pyramid's cross - section (when cut parallel to the base or in a way that involves the rectangular faces) is rectangular (or square, a special case of rectangle). When cut parallel to the base, it's a square (rectangular). If cut vertically through the apex and base edge, it can be triangular, but for the main cross - section related to rectangular/circular, the relevant cross - section (like parallel to the base or along the lateral faces) is rectangular.

Step2: Analyze Rectangular Prism

A rectangular prism has rectangular cross - sections. No matter how we cut it (parallel to the faces), the cross - section will be a rectangle (or square if the prism is a cube).

Step3: Analyze Cone

A cone, when cut parallel to its base, has a circular cross - section. The base of the cone is a circle, and a cross - section parallel to the base will be congruent to the base (a circle).

Step4: Analyze Cylinder

A cylinder, when cut parallel to its bases, has a circular cross - section. The two bases of the cylinder are circles, and a cross - section parallel to the bases is a circle. When cut vertically (along the axis), it has a rectangular cross - section, but for the circular/rectangular classification, the circular cross - section (parallel to the base) is a key one.

Step5: Analyze Triangular Prism

A triangular prism, when cut parallel to its rectangular faces (the lateral faces), has a rectangular cross - section. The lateral faces are rectangles, and a cross - section parallel to them will be a rectangle.

Step6: Analyze Cube

A cube is a special case of a rectangular prism. All its cross - sections (parallel to the faces) are squares (which are rectangles) or other rectangles when cut at an angle (but for the basic classification of circular/rectangular, it has rectangular cross - sections).

Answer:

• Square Pyramid: Rectangular
• Rectangular Prism: Rectangular
• Cone: Circular
• Cylinder: Circular (when cut parallel to base) or Rectangular (when cut vertically)
• Triangular Prism: Rectangular
• Cube: Rectangular