Volume + derivation - math problems

Number of problems found: 9

  • Maximum of volume
    kuzel2 The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
  • Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
  • 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
  • Cylindrical container
    valec2 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
  • Rectangle pool
    basen Find dimensions of an open pool with a square bottom with a capacity of 32 m3 to have painted/bricked walls with the least amount of material.
  • Paper box
    box The hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box?
  • Sphere in cone
    sphere-in-cone A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
  • Cone
    diag22 Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
  • 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?

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