Body volume + right triangle - examples

  1. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  2. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  3. Cuboid
    cuboid Cuboid with edge a=6 cm and body diagonal u=35 cm has volume V=1980 cm3. Calculate the length of the other edges.
  4. 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.
  5. 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.
  6. Cone
    cone-blue Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
  7. 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.
  8. Circular pool
    arc_open The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  9. Tetrahedral pyramid
    jehlan_1 Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.
  10. Rotary cone
    cone_3 The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
  11. 4side pyramid
    ihlany Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
  12. 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?
  13. Tetrahedral pyramid
    pyramid_4s Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
  14. Cut and cone
    kuzel Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
  15. Triangular pyramid
    tetrahedron1 Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
  16. Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
  17. Pentagonal pyramid
    pyramid-pentagon Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
  18. 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.
  19. Hexagonal prism
    hexa_prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
  20. Triangular prism
    hranol_3 Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.

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