Question

here is a cube:
blue cube image
what two of the following shapes of cross - sections could we create by slicing the cube diagonal to one of its faces?
choose 2 answers:
a triangle
b shape with two edges, one straight and one curved
c rectangle
d circle

Explanation:

• A cube has all edges equal and faces as squares. When slicing diagonally to a face, if we slice from one vertex to the opposite vertex of a face (but in 3D, a diagonal slice can be through three vertices forming a triangle, or through four vertices forming a rectangle).
• A triangle can be formed by slicing through three vertices (e.g., from one corner of the top face to two opposite corners of the bottom face).
• A rectangle can be formed by slicing through four vertices, parallel to a space - diagonal but in a way that the cross - section has four right angles (e.g., slicing through the mid - points of four edges that form a rectangle).
• A circle or a shape with one straight and one curved edge is impossible because a cube has only straight edges and flat faces, so slicing it will not produce curved edges or a circle.

Answer:

A. Triangle
C. Rectangle