Solid geometry, stereometry - page 14Solid 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.
- Sphere radius
The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
- Cuboid box
Cuboid box have dimensions of 30 cm, 25 cm and 40 cm. Sketch its network and compute surface area of box.
- Volume increase
How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
- Cylindrical tank
Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
- 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.
- Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
- Volume and area
What is the volume of a cube which has area of 361 cm2?
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)
- Two cuboids
Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
- 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?
- Cubes into cuboid
How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8,4dm and 4,8?
- 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?
- Inscribed sphere
How many percents of the cube volume takes the sphere inscribed into it?
- 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?
The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
- Volume of cube
Solve the volume of a cube with width 26cm .
- 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)
- 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?
- 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.
- 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.
See also more information on Wikipedia.