Billiard balls

A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. These balls form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single ball resting on top. If the bottom layer contains 16 balls, what is the height of the pile.

Correct answer:

h =  39.6408 cm

Step-by-step explanation:

r=6.35 (2x)2=(6r)2+(6r)2 x2=18r2 x=18 r=18 6.3526.9408 h12+x2=(6r)2 h1=(6 r)2x2=(6 6.35)226.9408226.9408 h=2 r+h1=2 6.35+26.9408=39.6408 cm



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions:

  • Distance of points
    jehlan_4b_obdelnik_1 A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
  • Tangent spheres
    tangent_spheres A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and
  • 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.
  • Hexagon cut pyramid
    pravkomoly Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm.
  • Tetrahedral pyramid
    jehlan_3 It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
  • Sphere and cone
    cone_in_sphere Within the sphere of radius G = 33 cm inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
  • Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
  • 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 sidewall and the base plane.) S =? , V =?
  • Inscribed circle
    Cube_with_inscribed_sphere A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
  • Cube in sphere
    sphere4 The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius.
  • Spherical cap
    Spherical_cap The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
  • Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  • Nice prism
    diagonal_rectangular_prism.JPG Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
  • Regular quadrilateral pyramid
    ihlan_rez What is the volume of a regular quadrilateral pyramid if its surface is 576 cm2 and the base edge is 16 cm?
  • Cube diagonals
    krychlicka_1 Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
  • Height of pyramid
    ihlan The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
  • Space diagonal angles
    kvadr_diagonal Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.