Max - cone

From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone.
a) Calculate cone volume.
b) Calculate the waste.

Result

V =  100.64 cm3
x =  322.01 cm3

Solution:

V1=13π(min(6.2,10)/2)26.2=62.394124495396 cm3 V2=13π(min(10,6.2)/2)26.2=62.394124495396 cm3 V3=13π(min(6.2,6.2)/2)210=100.63568466999 cm3 V=max(V1,V2,V3)=100.64 cm3V_1 = \dfrac13 \pi (\min(6.2, 10)/2)^2 \cdot 6.2 = 62.394124495396 \ cm^3 \ \\ V_2 = \dfrac13 \pi (\min(10, 6.2)/2)^2 \cdot 6.2 = 62.394124495396 \ cm^3 \ \\ V_3 = \dfrac13 \pi (\min(6.2, 6.2)/2)^2 \cdot 10 = 100.63568466999 \ cm^3 \ \\ V = \max(V_1,V_2, V_3) = 100.64 \ cm^3
x=6.2 10 6.262.394124495396=322.01 cm3x=6.2 \cdot \ 10 \cdot \ 6.2- 62.394124495396 = 322.01 \ cm^3



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





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




Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.

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

Next similar math problems:

  1. Pebble
    koule_krychle The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
  2. 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
  3. 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.
  4. Minimum surface
    cuboid_20 Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
  5. Surface of cubes
    cubes3_6 Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
  6. Body diagonal
    krychle_12 Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
  7. Cube into sphere
    cube_sphere_in The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  8. Alien ship
    cube_in_sphere The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
  9. 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?
  10. Prism 4 sides
    kvader11_5 Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
  11. Children's pool
    bazen2_17 Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m2 of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool?
  12. 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.
  13. Bricks pyramid
    The_Great_Pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
  14. 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.
  15. Equilateral cylinder
    sphere_in_cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
  16. The volume
    cuboid_17 The volume of a solid cylinder is 260 cm3 the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
  17. Solid cuboid
    cuboid_18 A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.