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 result:

a =  4835.9759 m

Solution:

$$\begin{gathered} r=3000\text{ m } \\ V={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 3000^3=113097335529{\text{m}}^3 \\ V=abc=a^3 \\ a=\sqrt[3]{V}=\sqrt[3]{113097335529}=4835.9759\text{ m} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Secret treasure
  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. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
• Rectangle pool
  Determine dimensions of open pool with a square bottom with a capacity 32 m³ to have painted/bricked walls with least amount of material.
• Prism X
  The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm³. What is the area of surface of the prism?
• Pyramid cut
  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
• Cube cut
  In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
• Cube in a sphere
  The cube is inscribed in a sphere with volume 7253 cm³. Determine the length of the edges of a cube.
• Prism bases
  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.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The heig
• Cardboard box
  Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long. Julia cut four squares with a side of
• Cone
  Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
• Body diagonal
  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?
• Cone
  Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
• Tower model
  Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
• Cubes
  One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm².
• TV transmitter
  The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?
• Prism
  Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube's s