Question

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.

Answer 1

Cone

Explanation:

Options:

a) Cone b) Cube c) Cylinder d) Triangular prism

From the given options (a) to (d), option (a) is true.

This is so, because.

The volume (V) of a cone is:

`V_1 = (1)/(3)\pi r^2h`

This is as a result of dilating the cylinder by 1/3 whose volume is:

`V_2 = \pi r^2h`

In other words:

`V_1 = (1)/(3)V_2`

i.e. the cross-section of the cylinder (V2) being dilated by 1/3 (which is between 0 and 1) gives the cone (V1)