# 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. Garden pond Concrete garden pond has bottom shape of a semicircle with a diameter 1.7 m and is 79 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 28 cm?
2. Iron sphere Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
3. Cuboid aquarium Cuboid 25 times 30 cm. How long is third side if cuboid contains 30 liters of water?
4. Sphere in cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
5. Cone Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
6. Cylinder - h2 Cylinder volume is 2.6 liters. Base area is 1.3 dm2. Calculate the height of the cylinder.
7. Water reservoir The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
8. Workers Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 12 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit?
9. Three dice When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
10. Cross-sections of a cone Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
11. Medal Calculate the approximate weight of the gold Olympics medal, if its diameter is 8 cm and a thickness 6 mm. The density of gold find out in the tables or on the Internet.
12. Tank The tank bottom has dimensions of 1.5 m and 3 2/6 m. The tank is 459.1 hl of water. How high is the water surface?
13. Reservoir + water Reservoir completely filled with water weighs 12 kg. After pouring off three quarters of the amount of water weights 3 kg. Calculate the weight and volume of the reservoir.
14. Sugar - cuboid Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet
15. Liters in cylinder Determine the height at which level 24 liters of water in a cylindrical container having a bottom diameter 36 cm.
16. Sportsman A trained athlete is able to exhale after a deep breath still 500 ml of air. At normal inhalation and exhalation is breathing 500 ml of air. Within one minute, one breath and exhaled 14 times. What part of breathing air per day is one exhalation?
17. Barrel 2 Empty barrel weighs 7 kg. When it filled with water up to 45% height, weighs 60 kg. How heavy is barrel full of water?
18. Tetrapack How high should be the milk box in the shape of a prism with base dimensions 8 cm and 8.8 cm if its volume is 1 liter?
19. Total displacement Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back
20. Leveling Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m2 to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness.

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