# 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. Three cubes The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
2. Excavation Excavation for the base of the cottage 4.5 m x 3.24 m x 60 cm. The excavated soil will increase its volume by one-quarter. Calculate the volume of excavated soil.
3. Container The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
4. Cardboard How many m2 of cardboard are needed to make the cuboid with dimensions 40 cm 60 cm and 20 cm?
5. Sheet of paper Is the sheet of paper measuring 18 and 25 cm enough for taping 9 cm cubes with an edge? (1 = yes, 0 = no)
6. Cube surface area The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased.
7. Two cuboids Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
8. Clay How many cubic centimeters of clay is in a pit of dimensions 4 m x 3 m x 3 m?
9. Cuboid Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
10. Surface of cuboid Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
11. Volume of cube Solve the volume of a cube with width 26cm .
12. Cuboid edges in ratio Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
13. Cuboid walls Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
14. Cuboid height What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
15. Hollow sphere The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
16. Metal pyramid Find the weight of a regular quadrilateral pyramid with a 5 cm length and 6,5 cm body height is made from material with density g/cm3.
17. 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?
18. Cremons The freight wagon is shaped like cuboid 21m and 3.5m and 4.2m How many cremons can be loaded if one is a cube with an edge length of 7 cm?
19. Stones in aquarium In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
20. Flowerbed The flowerbed has a length 3500mm and a width 1400mm. How many foil is needed to covers the flowerbed? How many m2 of foil was consumed for its production (add 10% of the material to the joint and waste)? How many liters of air is inside the enclosure? (

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