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Math Exercises: Metric Relations in Space

 

 

 

 

1. Consider a cube ABCDEFGH, |AB| = a = 4 cm. Find the distance from a point F to a given straight line :

 

a) AB b) AC c) AD d) AH e) AG

 

2. Consider a cuboid ABCDEFGH, |AB| = a = 60 cm, |AD| = b = 400 mm, |AE| = c = 8 dm. Find the distance from a point B to a point H, distance from a point D to a point G and the distance from a point C to a point F.

 

3. Consider a cone with a base diameter of d = 12 cm. Any point on the circumference of the base is located 8.5 cm from the apex of the cone. Find the distance from the apex V to the base.

 

4. Consider a truncated pyramid ABCDEFGH with square bases. Find the distance between planes ABCD and EFGH, if you know |AC| = 13 cm, |FH| = 9 cm and |AG| = 15 cm.

 

5. Consider a triangular prism ABCDEF with a base of right triangle, which has the right angles at the vertices C and F. The lengths of legs are |AC| = 8 m, |BC| = 6 m and a height of the prism is h = 15 m. Find the distance between points E and S and the size of an angle φ = |∠BSE|, where S is the midpoint of an edge AC.

 

6. Consider a cube ABCDEFGH with the points on its edges XEH, YAB, ZGH, if we know |EH| = |XH|, |AY| = |YB|, |ZH| = 3|GZ|. Find the angle between the straight lines AX and YZ.

 

7. Consider a cube ABCDEFGH. Let M be a midpoint of an edge AE and the size of a cube's edge is a. Find the angle between the straight lines BH and BM.

 

8. Consider a regular square pyramid ABCDV, |AB| = a, |AV| = a. Find the angle between two adjacent slant faces of the pyramid.

 

9. Consider a cube ABCDEFGH. Find out whether the planes DBH and ACF are perpendicular to each other.

 

10. Consider a regular hexagonal pyramid ABCDEFV, where |AB| = a, |AV| = 2a and a point M is the midpoint of the edge AV. Find the distance from the point M to the straight line DV.

 

11. Consider a cuboid ABCDEFGH. Find the distance from the straight line AC to the straight line FH and the volume of a cuboid, if |AG| = 5, |AC| = 3, |AH| = Square root of twenty.

 

12. Consider a cube ABCDEFGH, where |AB| = a = 5 cm, point M is the midpoint of the edge EF, point K is the midpoint of the edge CD. Find the distance from the plane BMG to the plane HAK.

 

13. Consider a regular square pyramid ABCDV, where |AB| = a = 4 cm, |AV| = b = 6 cm. Find the angle between two planes BCV and ABC.

 

14. Consider a cube ABCDEFGH, let a point K be the midpoint of the edge FG. Find out whether the planes ADK and DCH are perpendicular to each other.

 

15. Consider a regular tetrahedron ABCD, |AB| = a. Find the distance between two straight lines on which lie opposite edges of the tetrahedron.

 

 

 

 

 

 

You might be also interested in:

- Perimeter and Area of Plane Figures

- Volume and Surface Area of Solids

- Triangles and Properties of a Triangle

- Trigonometry

 

 
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