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.
The annual average rainfall in India was in Cherrapunji in the year 1981 26 461 mm. How many hectoliters of water fell on 1 m2? Would fit this amount of water into a cube of three meters?
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?
- Cube surface area
Wall of cube has content area 99 cm square. What is the surface of the cube?
- Tank diameter
A cylindrical tank has a volume of 60 hectoliters and is 2.5 meters deep. Calculate the tank diameter.
- 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
- 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?
The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
- 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?
- Volume of cube
Solve the volume of a cube with width 26cm .
- 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?
- Volume and body diagonal
Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
- How much
How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
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