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

Answer:

Cone

Step-by-step 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:

$V_1 = \frac{1}{3}\pi r^2h$

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

$V_2 = \pi r^2h$

In other words:

$V_1 = \frac{1}{3}V_2$

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