Sphere vs cube

How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?

Result

p =  63.662 %

Solution:

r=12 S1=4π⋅ r2=4⋅ 3.1416⋅ 122≐1809.5574 a=2⋅ r/3=2⋅ 12/3≐8 3≐13.8564 S2=6⋅ a2=6⋅ 13.85642=1152 p=S2/S1⋅ 100=1152/1809.5574⋅ 100≐63.662≐63.662%r=12 \ \\ S_{1}=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 12^2 \doteq 1809.5574 \ \\ a=2 \cdot \ r/\sqrt{ 3 }=2 \cdot \ 12/\sqrt{ 3 } \doteq 8 \ \sqrt{ 3 } \doteq 13.8564 \ \\ S_{2}=6 \cdot \ a^2=6 \cdot \ 13.8564^2=1152 \ \\ p=S_{2}/S_{1} \cdot \ 100=1152/1809.5574 \cdot \ 100 \doteq 63.662 \doteq 63.662 \%

Try another example


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
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:


 

 

 

Next similar math problems:

  1. Cube from sphere
    sphere_cube What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
  2. Sphere area
    sphere A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
  3. Kostka
    sphere_in_cube Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
  4. Cube in sphere
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
  5. Tangent spheres
    tangent_spheres A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor an
  6. Earth's surface
    earth_globe The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?
  7. Fit ball
    fitball What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
  8. Cube corners
    polyhedra-truncated-cube From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
  9. Cube surface area
    cubes2_2 The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased.
  10. Researchers
    house Researchers ask 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the families
  11. Summerjob
    tree2 The temporary workers planted new trees. Of the total number of 500 seedlings, they managed to plant 426. How many percents did they meet the daily planting limit?
  12. Profit gain
    percent_12 If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:
  13. Percentage increase
    percent_31 Increase number 400 by 3.5%
  14. Adding percentages
    percent 55%+36%+88%+71%+100=63% what is whole (X)? Percents can be added directly together if they are taken from the same whole, which means they have the same base amount. .. . You would add the two percentages to find the total amount.
  15. Borrowing
    test_5 I borrow 25,000 to 6.9% p.a.. I pay 500 per month. How much will I pay and for how long?
  16. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  17. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.