# 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.

Alaska is the largest state in the United States and has a surface area of approximately 588,000 square miles. Montana has a surface area that is approximately 25% of the surface area of Alaska. What is the approximate surface area of Montana?
2. Inscribed
Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
3. Circular pool
The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
4. 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. In what ratio are the volumes of cube, cuboid, and sphere?
5. Inscribed sphere
How many percents of the cube volume takes the sphere inscribed into it?
6. Basen
How many square meters of tiles we need to tile the walls and floor of the pool 15 meters long, six meters wide and two meters?deep
7. Cubes into cuboid
How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8,4dm and 4,8?
8. Rectangular prism
If i have a rectangular prism with a length of 1,000 cm, width of 30 cm and a height of 50 cm, what is the volume?
9. Rain
It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
10. A residential
A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, th
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. How much
How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
13. Cuboid
The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
14. Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
15. Cylinder-shaped vase
If the cylinder-shaped vase is filled with water up to 35 cm, it contains 1 liter of water. How much water will it contain if it is filled to a height of 45cm?
16. Water tank
A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
17. Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
18. 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?
19. Volume and body diagonal
Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
20. Rainfall
A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.

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