# Solid geometry, stereometry - page 14

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.

The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
2. Cuboid box
Cuboid box have dimensions of 30 cm, 25 cm and 40 cm. Sketch its network and compute surface area of box.
3. Volume increase
How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
4. Cylindrical tank
Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
5. Cube 1-2-3
Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
6. Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
7. Volume and area
What is the volume of a cube which has area of 361 cm2?
8. Cuboids
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
9. Two cuboids
Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
10. Surface of cubes
Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
11. Cubes into cuboid
How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8,4dm and 4,8?
12. Scale factor
A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
13. Inscribed sphere
How many percents of the cube volume takes the sphere inscribed into it?
14. Water block
A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
15. Ratio
The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
16. Volume of cube
Solve the volume of a cube with width 26cm .
17. Stones in aquarium
In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
18. Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
19. Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
20. Cuboid - Vab
Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters.

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