Question

the cross section of a solid figure sliced perpendicular to its base is shown.
decide whether or not the cross section could have come from each of the figures listed below

	yes	no
cube	○	○
square pyramid	○	○
triangular prism	○	○
rectangular prism	○	○

Explanation:

Step1: Analyze Cylinder

A cylinder's cross - section perpendicular to the base (which is a circle) is a rectangle (or square if the height equals the diameter). The given cross - section is a square (with right angles and equal sides), so a cylinder can have this cross - section. So for cylinder, mark Yes.

Step2: Analyze Cube

A cube, when sliced perpendicular to its base, will have a square cross - section (since all faces are squares). So for cube, mark Yes.

Step3: Analyze Square Pyramid

A square pyramid, when sliced perpendicular to its base (a square), the cross - section will be a triangle (if sliced from the apex to the base) or a trapezoid (if sliced parallel to the base but not at the base). A square cross - section perpendicular to the base is not possible for a square pyramid. So for square pyramid, mark No.

Step4: Analyze Triangular Prism

A triangular prism has a triangular base. When sliced perpendicular to its base, the cross - section will be a triangle or a rectangle (if the base is a right - triangle). A square cross - section perpendicular to the base is not possible for a triangular prism. So for triangular prism, mark No.

Step5: Analyze Rectangular Prism

A rectangular prism, if it is a cube (a special case of rectangular prism) or if the length and width of the base are equal and the height is equal to them, when sliced perpendicular to the base, will have a square cross - section. So for rectangular prism, mark Yes.

Answer:

• cylinder: Yes
• cube: Yes
• square pyramid: No
• triangular prism: No
• rectangular prism: Yes