# 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. Water flow How much water flow in pipe with a diameter of 16 cm in 1 hour if the water velocity is 2.5 m/s?
2. Kitchen Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
3. 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?
4. Cube containers Two containers shaped of cube with edges of 0.7 m and 0.9 m replace a single cube so that it has the same volume as the original two together. What is the length of the edges of the new cube?
5. Earth's surface The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?
6. Prism bases Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
7. Oak cuboid Oak timber is rectangular shaped with dimensions of 2m, 30 cm and 15 cm. It weight is 70 kg. Calculate the weight 1 dm³ of timber.
8. Water reservoir The water tank has a cuboid with edges a= 1 m, b=2 m , c = 1 m. Calculate how many centimeters of water level falls, if we fill fifteen 12 liters cans.
9. 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?
10. Building Lenka has 22 cubes for the construction of building comprising three cubes in height, the width of two cubes, and the length of four cubes. Is she able to build an building with these cubes?
11. Surface area 2 Calculate how many % reduce the surface area of the cube is we reduced length of each edge by 10%.
12. Cube 6 Surface area of one wall cube is 1600 cm square. How many liters of water can fit into the cube?
13. The cube - simple Calculate the surface of the cube measuring 15 centimeters.
14. Cube 5 The surface of the cube is 15.36 dm2. How will change the surface area of this cube if the length of the edges is reduced by 2 cm?
15. Cubes - diff Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
16. 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?
17. Railway wagon The railway wagon holds 75 m3 load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons?
18. 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.
19. Aquarium volume The aquarium has a cuboid shape and dimensions a = 0.3 m, b = 0.85 m, c =? , V = ?. What volume has a body, if after dipping into the aquarium water level rises by 28 mm?
20. Rain How many mm of water rained the roof space 75 m2 if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-)

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...