Hole

In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?

Result

D =  8.2 cm

Solution:

h=14 V1=0.27V2 π(D2)2h=0.27h3  D=2h0.27/π=8.2  cm h=14 \ \\ V_1 = 0.27 \cdot V_2 \ \\ \pi(\dfrac{ D}{2} )^2 \cdot h = 0.27 \cdot h^3 \ \\ \ \\ D=2h\sqrt{ 0.27/\pi} = 8.2 \ \text { cm }







Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

  1. Center of the cube
    center_of_cube Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
  2. Transforming cuboid
    cube Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
  3. Cubes
    rubik_cube Cube, which consists of 27 small cubes with edge 4 dm has volume:
  4. Granite cube
    cube_3 What is the weight in kg granite cube with an edge of 0.5 m if 1dm3 of granite weight 2600 g?
  5. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
  6. Lathe
    soustruh From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
  7. Tereza
    cube The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
  8. Cube zoom
    krychle_1 How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
  9. Lead cube
    pb_cube Calculate the edge of the cube made ​​from lead, which weighs 19 kg. The density of lead is 11341 kg/m3.
  10. Mouse Hryzka
    myska_hryzka Mouse Hryzka found 27 identical cubes of cheese. She first put in a large cube out of them and then waited for a while before the cheese cubes stuck together. Then from every wall of the big cube she will eats the middle cube. Then she also eats the cube
  11. Space diagonal
    cube_diagonals The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
  12. 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 257 mm2.
  13. Cube
    kocka_rubik The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
  14. Cube in ball
    sphere2 Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
  15. Cuboid
    kvadr Find the cuboid that has the same surface area as the volume.
  16. Volume from surface area
    cube_3 What is the volume of the cube whose surface area is 96 cm2?
  17. Cone in cube
    kuzel_kocka The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage.