Solids > Series of parallel cross sections
12345Series of parallel cross sections

Solutions to the exercises

Exercise 1
a

See the figure.

b

See figure at a.

c

That consists only of point E .

Exercise 2

It is easiest to do this in a top view.
See below.

Exercise 3

These are cross-sections of a cone with radius 3 cm and a height of 3 cm.

Exercise 4

See the figure.

Exercise 5

Using a top view you can measure or compute the width of each cross-section.
The first cross-section is a point.
The second cross-section has a width of 3 2 - 2 2 = 5 cm and a height of 1 3 5 = 1 2 3 cm and the shape of a parabola.
The third cross-section has a width of 3 2 - 1 2 = 8 cm and a height of 2 3 5 = 3 1 3 cm and also has the shape of a parabola.
The fourth cross-section is a isosceles triangle with a base of 6 cm and a height of 5 cm.
The fifth cross-section is equal to the third, The sixth is equal to the second and the seventh cross-section is a point again.

Exercise 6

In a view you can calculate or measure he width of each cross-section.
The first cross-section is a point.
The second cross-section is a circle with radius 3 2 - 2 2 = 5 cm.
The third cross-section is a circle with radius 3 2 - 1 2 = 8 cm.
The fourth cross-section is a circle with radius 3 cm.
The fifth cross-section is equal to the third, The sixth is equal to the second and the seventh cross-section is a point again.

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