Let's consider each set of slices and visualize the type of solid they could come from:
a. A set of similar rectangles decreasing in size to a single point, ordered from greatest in size to smallest:
When we visualize this pattern, we could imagine the rectangles reducing in one dimension as they approach a vertex, similar to the way a party hat or ice cream cone narrows to a point. This is characteristic of a cone, which has a circular base and narrows to a point called the apex.
b. A set of congruent triangles:
For a set of congruent triangles to come from a three-dimensional solid, they would typically make up the two ends of the solid. Since the triangles are congruent, the solid must maintain a consistent cross-section along its length. This describes a triangular prism, which has the same triangle at both ends and rectangular faces joining them.
c. A set of congruent squares:
If we have a set of congruent squares, then stacking them directly on top of each other without any changes in size or angle would form a solid with equal length, width, and height. This is the definition of a cube, where each face is a square and all edges are the same length.
d. A set of circles, decreasing in size to a single point, ordered from greatest in size to smallest:
Imagine slicing a spherical object, like a ball or an orange, from outside in. The slices would start as large circles from the equator of the sphere and then decrease in size as you move towards the poles. Eventually, the slices would reduce to a single point at the top and bottom of the sphere. This describes a sphere, which is perfectly round and symmetrical in all directions.
Therefore, the solids corresponding to each set of slices are:
a. Cone
b. Triangular prism
c. Cube
d. Sphere
