carol wants to make a model of a prsm whose base has 9 sides. she will use alls of clay for the vertices and straws for the edges. How many balls of clay and straws will she need? how many faces will her prism have?
To find the number of balls of clay Carol will need, we need to determine the number of vertices of the prism. Since the prism's base has 9 sides, it means that the base has 9 vertices. And since a prism has two identical bases, there will be 9 vertices for the top base as well. Therefore, the total number of vertices is 9 + 9 = 18.
Hence, Carol will need 18 balls of clay for the vertices.
Now, let's determine the number of straws she will need. Each edge of the prism corresponds to an edge of the base, and since the base of the prism has 9 sides, it will have 9 edges. Moreover, there is one more edge joining the corresponding vertices of the top and bottom bases. Therefore, the total number of edges will be 9 + 1 = 10.
Thus, Carol will need 10 straws for the edges.
Finally, let's calculate the number of faces the prism will have. A prism has two identical bases, which means there are 2 faces contributed by the bases. Additionally, each side of the base contributes 1 face to the prism. Since the base has 9 sides, there will be 9 additional faces. Therefore, the prism will have 2 + 9 = 11 faces.
So, Carol will need 18 balls of clay for the vertices, 10 straws for the edges, and her prism will have 11 faces.