Alien ship

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 largest possible volume.

Correct answer:

a =  4835.9759 m

Step-by-step explanation:

r=3000 m  V=43 π r3=43 3.1416 30003=113097335529 m3  V=abc=a3  a=V3=1130973355293=4835.9759 m



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






avatar




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

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

Related math problems and questions:

  • 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.
  • Rectangle pool
    basen_5 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.
  • Prism bases
    hranoly Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2. Determine the area of the base and walls of the prism.
  • Cube-shaped box
    milk_1 The cube-shaped box is filled to the brim with 2 liters of milk. Calculate the edge and surface of the box.
  • Regular square prism
    cuboid_3colors_1 The volume of a regular square prism is 192 cm3. The size of its base edge and body height are 1: 3. Calculate the surface of the prism.
  • Cylindrical container
    valec2_6 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.
  • Prism X
    Cuboid_simple The prism with the edges of the lengths x cm, 2x cm, and 3x cm has volume 20250 cm3. What is the area of the surface of the prism?
  • Body diagonal
    kvader11_1 The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
  • The ball
    sphere4 The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
  • Cube in ball
    sphere2 Cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of cube of the volume of the sphere?
  • Hollow sphere
    sphere_2 The steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and the density of steel is 7850 kg/m3
  • Stadium
    sphere_segment A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
  • 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?
  • Balls
    balls_1 Ping pong balls have a diameter of approximately 5.1 cm. It sold in boxes of 10 pieces: each box has a cuboid shape with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled with balls.
  • Concrete block
    abc Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
  • Surface and volume od cuboid
    kvader Content area of the square base of cuboid is Sp = 36 cm2 and its height 80 mm. Determine its surface area and volume.
  • Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with a volume 7253 cm3. Determine the length of the edges of a cube.