# 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. Airplane Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
2. The tank The tank has 1320 liters of water. The tank has the shape of a prism, its base is an rectangle with sides a = 0,6 m and b = 1,5 m. How high does the water level reach in the tank?
3. Juice box The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
4. Square prism Calculate the volume of a square prism of high 2 dm wherein the base is: rectangle with sides 17 cm and 1.3 dm
5. Flowerbed Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
6. 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. 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
8. 3sides prism The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
9. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
10. Pyramid 8 Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
11. 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.
12. Triangular pyramid Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
13. Rotary cylinder The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
14. Cylinder surface, volume The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
15. Rope How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
16. Similarity Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity.
17. Church roof The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
18. Trough How many liters of water per second can go via trough, which has a cross section of semicircle with radius 2.5 m and speed of water is 147 cm per second?
19. Tetrahedral pyramid It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
20. Sphere vs cube How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?

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