# 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.

#### Number of problems found: 981 The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
• Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
• Copper winding Calculate the current flowing through the copper winding at an operating temperature of 70°C. Celsius, if the winding diameter is 1.128 mm and the winding length is 40 m. The winding is connected to 8V. Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
• Paper box Calculate whether 11 dm² of paper is sufficient for gluing a box without a lid with bottom dimensions of 2 dm and 15 cm and 12 cm high. Write result as: 0 = No, 1 = Yes
• 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?
• Trapezoidal prism Calculate the volume of a prism with a trapezoidal base with side a = 6dm, side c = 4 dm, height of the prism = 8dm. The height of the trapezoid is va = 3dm.
• Surface area The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
• Office Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400?
• Tropical, mild and arctic How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.
• Water tank What is the height of the cuboid-shaped tank with the bottom dimensions of 80 cm and 50 cm if the 480 liters of water reaches 10 cm below the top?
• Concrete box The concrete box with walls thick 7 cm has the following external dimensions: length 1.8 m, width 44 cm and height 46 cm. How many liters of soil can fit if I fill it to the brim?
• Tetrahedral pyramid Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
• Cube, cuboid, and sphere Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. At what rate are the volumes of cube, cuboid, and sphere?
• Velocity ratio Determine the ratio at which the fluid velocity in different parts of the pipeline (one part has a diameter of 5 cm and the other has a diameter of 3 cm), when you know that at every point of the liquid is the product of the area of tube [S] and the fluid
• Water container Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container?
• Iron fence One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3. The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
• 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
• Pizza Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?

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