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12345Series of parallel cross sections

Exercises

Exercise 1

Shown is a prism $A B C . D E F$ that has two square sides. These squares have edges of $4$ cm. Furthermore it is given that: $∠ B A C = 90 °$ , $B G = 1$ and $C H = 1$ .

Construct a cross-section through point $B$ and parallel with plane $G H D$ .

Construct a cross-section through the center of $M$ of $B E$ and parallel to plane $G H D$ .

What does a cross-section of a plane through $E$ and parallel with plane $G H D$ look like?

Exercise 2

Of this eight sided figure $A B C D . E F G H$ the base $A B C D$ is a square of $4$ bij $4$ , the height is $4$ and the top side $D E F G$ a square with diagonals of $2$ units. A horizontal cross-section has been drawn through the centers of all upright edges of this figure.

Construct a series of five life sized cross-sections parallel to the drawn plane. The cross-sections are spaced $1$ unit apart and the drawn plane is one of the five cross-sections.

Exercise 3

A series of vertical cross-sections of a solid is shown here. The distance between the cross-sections is $0,5$ cm.

Draw a parallel projection of this solid.

Exercise 4

Here you see the cross-section of the plane through $P$ , $Q$ and $R$ and the regular three sided prism $A B C . D E F$ .

Use this to draw a parallel cross-section through point $A$ and a cross-section parallel to this through the center $M$ of edge $B E$ .

Exercise 5

Draw a series of parallel cross-sections of a cone, parallel to its axis. The distance betwee the cross-sections is $1$ cm. the cone has a height of $5$ cm and the radius of the base circle is $3$ cm. Show your approach, give any necessary calculations.

Exercise 6

Draw a series of parallel cross-sections of a sphere with radius $3$ cm. The distance between the cross-sections is $1$ cm. Show your approach, give any necessary calculations.

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