Body volume - examples

  1. Cube into sphere
    sphere_in_cylinder_1 The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  2. Hemispherical hollow
    odsek The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
  3. Equilateral cylinder
    sphere_in_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.
  4. An oil
    valec2_13 An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
  5. Stones in aquarium
    akvarko_15 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)
  6. The volume
    cuboid_17 The volume of a solid cylinder is 260 cm3 the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
  7. Triangular prism
    prism3s_1 Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
  8. Square prism
    lichob_2 Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
  9. Find the
    cuboid_16 Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
  10. The tank
    nadrz_15 The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?
  11. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.
  12. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  13. Cuboid
    cuboid Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm3. Calculate the length of the other edges.
  14. Cuboid
    cuboid_1 The cuboid has a surface area 1771 cm2, the length of its edges are in the ratio 5:2:4. Calculate the volume of the cuboid.
  15. Pool
    swimming-pool The swimming pool is 10 m wide and 22 m long and 191 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
  16. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
  17. 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 254 cm2.
  18. Transforming cuboid
    cube Cuboid with dimensions 10 cm, 17 and 17 cm is converted into a cube with the same volume. What is its edge length?
  19. Tereza
    cube The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
  20. Sphere
    1sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?

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