Question

practice 5 (from unit 5, lesson 3)
select the solid whose cross sections are dilations of some two - dimensional shape using a point directly above the shape as a center and scale factors ranging from 0 to 1.
a cone
b cube
c cylinder
d triangular prism

Explanation:

To solve this, we analyze each option:

• Option A (cone): A cone has a circular base. When we take cross - sections parallel to the base (using the apex as the center of dilation, which is directly above the base), the cross - sections are circles. The radius of these circular cross - sections decreases as we move from the base towards the apex. The scale factor of dilation (ratio of the radius of the cross - section to the radius of the base) ranges from 1 (at the base) to 0 (at the apex). So, the cross - sections are dilations of the circular base with the apex as the center and scale factors from 0 to 1.
• Option B (cube): The cross - sections of a cube (e.g., when cut parallel to a face) are congruent squares. There is no dilation with scale factors from 0 to 1 because the size of the cross - section (the square) remains the same (scale factor = 1) when cut parallel to a face, and for other cuts, the relationship is not a dilation with scale factors in [0,1] centered above the shape.
• Option C (cylinder): The cross - sections of a cylinder parallel to the base are congruent circles (scale factor = 1). There is no variation in scale factor from 0 to 1 as we move along the axis of the cylinder.
• Option D (triangular prism): The cross - sections parallel to the base are congruent triangles (scale factor = 1). There is no dilation with scale factors from 0 to 1 as we move along the length of the prism.

Answer:

A. cone