Question

A solid ‘star’ shape is created by gluing a square-based pyramid, in which each edge is of length 1 unit, precisely onto each face of a cube of edge 1 unit. How many faces does this ‘star’ have?

a. How many total faces does the 'star' shape have?
A) 6
B) 8
C) 10
D) 12

Answer 1

The 'star' shape has a total of 30 faces; 6 from the original cube and 24 from the six pyramids attached to the cube.

Step-by-step explanation:

To determine how many total faces the 'star' shape has, we consider the geometry of the solid. A cube has 6 faces. When a square-based pyramid is glued onto each of these, it adds more faces. The base of the pyramid, however, is not counted as a new face since it's glued to the cube. Each pyramid has 4 triangular faces. As there are 6 pyramids (one for each face of the cube), this results in 6*4 additional faces. So the total number of faces is the original 6 cube faces plus the 24 pyramid faces (6*4), which equals 30 faces in total.