# 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. Body diagonal Find the cube surface if its body diagonal has a size of 6 cm.
2. Prism - box The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
3. Church roof 2 The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
4. Painting The room is long 50 meters and wide 60dm and 300 cm high. Calculate how much it will cost painting if area of windows and doors is 15% of the total area. One square meter cost 50cents.
5. Concrete block Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
6. Costume Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand D
7. Hexagonal pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.
8. Rainfall How many liters of water did fell in a 32m long and 8m wide garden, if 8mm of rain fell?
9. Octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
10. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
11. Lamp cone Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
12. Truncated cone A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume.
13. Shell of cylinder Calculate the content of shell the 1.6 m height cylinder with a base radius of 0.4 m.
14. Prism The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
15. Triangular prism Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
16. Bricks wall There are 5000 bricks. How high wall thickness of 20 cm around the area which has dimensions 20 m and 15 m can use these bricks to build? Brick dimensions are 30 cm, 20 cm and 10 cm.
17. Prism Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
18. Decagon prism A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm3, round to two decimal places.
19. Hexa prism Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
20. Prism - eq triangle Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.

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