# Solid geometry, stereometry - page 10

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. Kitchen
Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
3. 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?
4. Cube volume
The cube has a surface of 384 cm2. Calculate its volume.
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. 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?
9. 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.
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. 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?
14. 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?
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. 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?
17. 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.
18. 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? :-)
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. The cube - simple
Calculate the surface of the cube measuring 15 centimeters.

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