# 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. Cremons The freight wagon is shaped like cuboid 21m and 3.5m and 4.2m How many cremons can be loaded if one is a cube with an edge length of 7 cm?
2. Tank diameter A cylindrical tank has a volume of 60 hectoliters and is 2.5 meters deep. Calculate the tank diameter.
3. Cube surface area Wall of cube has content area 99 cm square. What is the surface of the cube? The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
5. Cuboid box Cuboid box have dimensions of 30 cm, 25 cm and 40 cm. Sketch its network and compute surface area of box.
6. Cube 1-2-3 Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
7. Cylindrical tank Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
8. Volume increase How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
9. Three cubes The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
10. Volume and area What is the volume of a cube which has area of 361 cm2?
11. Surface of cubes Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
12. Cuboids Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
13. Two cuboids Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
14. Cubes into cuboid How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8,4dm and 4,8?
15. Inscribed sphere How many percents of the cube volume takes the sphere inscribed into it?
16. Water block A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
17. Scale factor A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
18. Ratio The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
19. Stones in aquarium In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
20. Volume of cube Solve the volume of a cube with width 26cm .

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