# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

1. Forces In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
2. Cylinders Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
3. MO SK/CZ Z9–I–3 John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
4. Rainfall Annual rainfall in our country are an average of 797 mm. How many m3 of water rains on average per hectare?
5. Prism Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
6. Cuboid diagonal Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
7. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
8. Spherical cap From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
9. Present Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
10. Cone Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
11. Earth parallel Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
12. Circular pool The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
13. Floating barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
14. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
15. Tower The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
16. Pyramid roof 2/4 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
17. Rotation of the Earth Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
18. Cap Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
19. Plastic pipe Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m3.
20. Cube - angles Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.

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