# 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. Glass aquarium How many m2 of glass are needed to produce aquarium with bottom dimensions of 70 cm x 40 cm and 50 cm high?
2. The cube The surface of the cube is 150 square centimeters. Calculate: a- the content of its walls b - the length of its edges
3. Cuboid - edges The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
4. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
5. Truncated cone 5 The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone? Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
7. 3s prism It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
8. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
9. 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 De
10. 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.
11. 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.
12. Wood lumber Wooden lumber is 4 m long and has a cross section square with side 15 cm. Calculate: a) the volume of lumber b) the weight of the lumber if 1 m3 weighs 790 kg
13. Common cylinder I've quite common example of a rotary cylinder. Known: S1 = 1 m2, r = 0.1 m Calculate : v =? V =? You can verify the results?
14. Megapascals What is the area of crosssection of the piston, if the force of 300 kN produces a pressure of 5 MPa?
15. Hexagonal prism 2 The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
16. Cuboid easy The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
17. Shell of cylinder Calculate the content of shell the 1.6 m height cylinder with a base radius of 0.4 m.
18. Roof 8 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
19. 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?
20. Painting a hut It is necessary to paint the exterior walls of hut whose layout is a rectangle of 6.16 m x 8.78 m wall height is 2.85 meters. Cottage has five rectangular windows; three have dimensions of 1.15 m x 1.32 m and two 0,45 m x 0.96 m. How many m2 is necessary

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