Diagonal + body volume - math problems

  1. Body diagonal
    kvadr_diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
  2. Right pyramid
    squarepyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
  3. Prism 4 sides
    hranol4sreg The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
  4. Axial cut of a rectangle
    cylinder_cut Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
  5. Prism diagonal
    hranol222_2 The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
  6. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  7. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  8. Body diagonal
    krychle_12 Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
  9. Angle of diagonal
    hranol_9 Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
  10. Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  11. Quadrangular pyramid
    komoly Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
  12. Quadrangular prism
    hranol4sreg_7 Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
  13. Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  14. Four sided prism
    hranol4sreg Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
  15. Hexagon rotation
    hexagnos A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
  16. Support colum
    pillar-diamond Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
  17. Cuboid - volume, diagonals
    prism_diagonals The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
  18. Concrete block
    abc Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
  19. Two balls
    balls-inside-cylinder Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
  20. Prism - box
    cuboids_1 The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.

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