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.

Number of problems found: 892

  • Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  • Cuboid diagonal
    cube_2 Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
  • Cuboid
    cuboid_diagonal Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
  • Task
    cube_1 I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal.
  • Rotating cone II
    cone Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
  • Rotary cone
    cone_2 Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
  • Tinsmith
    rury Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate?
  • Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.
  • Tank
    barrel_1 In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
  • Road embankment
    nasyp_cesta Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
  • Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
  • Gold wire
    gold_wire From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
  • Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
  • Diagonal
    krychle Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
  • Felix
    astronaut Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
  • Roller
    cylinder Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
  • Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  • Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  • Glass of juice
    glass_of_juice Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
  • Cap
    cone_hat Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.

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