Sphere - examples

  1. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 6598 cm3. Determine the length of the edges of a cube.
  2. 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 137 cm2.
  3. Sphere
    1sphere Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
  4. Spherical cap
    kulova_usec From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere?
  5. Earth parallel
    parallels Earth's radius is 6378 km long. Calculate the length parallel of latitude 50°.
  6. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  7. Rotation of the Earth
    earth_1 Calculate the circumferential speed of the Earth's surface at a latitude of 53.7°​​. Consider a globe with a radius of 6378 km.
  8. Sphere slices
    sphere_slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=37 cm, r2=40 cm and its distance v=20 cm.
  9. Hollow sphere
    Xmas_ball Calculate the weight of a hollow brass sphere (density 8.5 g/cm3), if the outer diameter is 10 cm and wall thickness is 3 mm.
  10. Cube in ball
    sphere2 Cube is inscribed into sphere of radius 136 mm. How many percent is the volume of cube of the volume of sphere?
  11. Balls
    steel_ball Three metal balls with volumes V1=41 cm3 V2=58 cm3 and V3=83 cm3 melted into one ball. Determine it's surface area.
  12. Balls
    balls_1 Ping pong balls have a diameter of approximately 3 cm. They are sold in boxes of 3 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled wit
  13. Sphere A2V
    sphere3 Surface of the sphere is 306 m2. What is its volume?
  14. Spherical segment
    circular_segment_1 Spherical segment with height h=8 has a volume V=294. Calculate the radius of the sphere of which is cut this segment.
  15. Sphere in cone
    sphere-in-cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
  16. Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 814 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
  17. Plasticine ball
    p_balls Plasticine balls have radius r1=100 mm, r2=48 cm. For these balls are molded one big ball. Calculate the radius r of the resulting ball.
  18. Sphere and cone
    cone_in_sphere Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
  19. Shots
    broky 2000 lead shots with diameter 2 mm is decanted into a ball. What is it diameter?
  20. Felix
    astronaut Calculate how much land saw Felix Baumgartner after jump from 22 km above ground. The radius of the Earth is R = 6378 km.

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