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. Sphere cuts
    sphere_cut At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
  2. Sphere slices
    sphere_slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
  3. Cylinder
    valec Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.
  4. 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.
  5. 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.
  6. Concrete pipe
    concrete_pipe Concrete pipe is cylindrical with an inner diameter 110 cm and outer 120 cm. Calculate the surface of the concrete pipe, if it is 9 m long.
  7. 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?
  8. Cylinder - basics
    cylinder Cylinder with base radius r = 45 dm and height h=22 dm. Calculate:
  9. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
  10. Present
    prezent Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
  11. Cube - angles
    cube_diagonal_1 Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
  12. Cube diagonal
    cube_diagonal Determine the length of the cube diagonal with edge 37 mm.
  13. Rotation of the Earth
    earth_1 Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.

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