Question

the shapes shown are different cross - sections of the same three - dimensional object. which three - dimensional object has these cross - sections?

Explanation:

• Option A (Cone): Cross - sections of a cone can be a circle (when cut parallel to the base), a triangle (when cut through the vertex and perpendicular to the base), but it cannot form a rectangle or a square.
• Option B (Cube): Cross - sections of a cube can be a square (when cut parallel to a face), a rectangle (when cut at an angle to the faces but not through the vertices in a non - triangular way), but it cannot form a triangle.
• Option C (Cylinder): Cross - sections of a cylinder can be a circle (when cut parallel to the bases) or a rectangle (when cut perpendicular to the bases), but it cannot form a triangle.
• Option D (Square - based pyramid):
• When cut parallel to the base, the cross - section is a square (if the base is square).
• When cut perpendicular to the base and through the vertex, the cross - section is a triangle.
• When cut at an angle to the base (not through the vertex in a non - triangular way), the cross - section can be a rectangle.

Answer:

D.