Solids

Exercise 1

Given is the cube $A B C D . E F G H$ with edges of $6$ cm. Point $P$ is the center of the edge $A E$ and point $Q$ is the center of $C G$ . The plane $P B Q H$ divides the cube into two solids, one of which is the solid $A B C D . P B Q H$ .

a

Draw the three views of $A B C D . P B Q H$ .

b

Draw the "net" of the solid $A B C D . P B Q H$ .

c

Calculate the size of the angles of the plane $P B Q H$ .

Exercise 2

Here you see a so called hipped roof, a roof with a rectangular base $A B C D$ with the roof-ridge $E F$ situated exactly over the middle of the base. The roof itself consists of twee equilateral triangles and two symmetric trapeziums.

a

Draw its three views.

b

Draw the "net" of this roof.

Exercise 3

The base of a pyramid $T . A B C D E$ is a regular pentagon $A B C D E$ . The height of the pyramid is $T S$ , where point $S$ is the center of the circle through the vertices of the base. All edges of this pyramid are $4$ cm.

a

Draw the three views of the pyramid $T . A B C D E$ . Show all necessary calculations.

b

Draw the "net" of this pyramid. Show all necessary calculations.

Exercise 4

Below you see the side view of a purely circular tent.

Draw a "net" of this tent on a scale of $1 : 100$ .

Exercise 5

Arab whirling dervishes often wear a so called cone skirt. That is a widening skirt that - if the cloth would be stiff - would have the shape of a truncated cone. Here you see the pattern (the "net") of such a cone skirt.

Draw a front view and a top view of the corresponding truncated cone. Show all necessary calculations.

Exercise 6

The figure you see here is a regular octagonal antiprism. You can find similar figures and their "nets" on the website korthalsaltes.com.
All edges of this antiprism are $5$ cm.

Draw an "net" of this antiprism.

Exercises