Body volume + right triangle - examples

  1. Quadrangular pyramid
    pyramid_4s_1 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
  2. Cube cut
    cut_cube In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
  3. 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.
  4. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  5. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  6. Cuboid
    cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
  7. 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.
  8. 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.
  9. 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°.
  10. 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.
  11. 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?
  12. 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.
  13. 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.
  14. 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.
  15. 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?
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.

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