Question

7. Suppose a student stacks 1000 congruent circles one on top of the other, and the teacher

1000 similar circles, with each circle a little smaller than the one below it.
a. What is the name of the solid formed by the stack of congruent circles?
b. Relate the dimensions of one of the congruent circles to the dimensions of this solic
c. What is the name of the solid formed by the stack of similar circles?
d. Relate the height of the stack of similar circles to a dimension of this solid.

Answer 1

See below.

Explanation:

a. That would be a cylinder.

b.The height of the cylinder will be n * thickness of one circle where n is the number of circles. The volume of the cylinder is π r^2 h where h is the height of the stack.

c. That would be a cone

d. The height of the cone will be n * thickness of one circle where n is the number of similar circles.

Volume of the cone = 1/3 * π r^2 h where h is the height of the stack of circles.