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.

Result

a =  4835.976 m

Solution:

r=3000 m  V=43 π r3=43 3.1416 30003=113097335529 m3  V=abc=a3  a=V3=11309733552934835.9759=4835.976  m r = 3000 \ m \ \\ \ \\ V = \dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3 = \dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 3000^3 = 113097335529 \ m^3 \ \\ \ \\ V = abc = a^3 \ \\ \ \\ a = \sqrt[3]{ V} = \sqrt[3]{ 113097335529 } \doteq 4835.9759 = 4835.976 \ \text { m }



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




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

Next similar math problems:

  1. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  2. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
  3. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  4. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.
  5. Pool
    pool If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
  6. TV transmitter
    praded 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.
  7. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
  8. Cuboid
    cuboid Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  9. Rectangle
    rectangle_inscribed_circle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
  10. Bonus
    moeny Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
  11. Logic
    blue-barrel A man can drink a barrel of water for 26 days, woman for 48 days. How many days will a barrel last between them?
  12. Beer
    piva After three 10° beers consumed in a short time, there is 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
  13. Circle chord
    circleChord What is the length d of the chord circle of diameter 51 mm, if the distance from the center circle is 19 mm?
  14. River
    kongo_river Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
  15. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  16. Clock
    hodiny How many times a day hands on a clock overlap?
  17. Server
    p_pro Calculate how many average minutes a year is a webserver is unavailable, the availability is 99.99%.