Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.

Result

V =  18984.5 dm3
S =  3441.5 dm2

Solution:

 v2=r12r22+v22v=312922+252225=137.56cm r=r22+v22=922+137.562=165.49cm  V=43πr3=431000π165.493=18984.5 dm3 \ \\ v_2 = \dfrac{ | r_1^2-r_2^2+v^2 | }{2v} = \dfrac{ | 31^2-92^2+25^2 | }{2 \cdot 25} = 137.56 cm \ \\ r = \sqrt{ r_2^2 + v_2^2 } = \sqrt{ 92^2 + 137.56^2} = 165.49 cm \ \\ \ \\ V = \dfrac{4}{3} \pi r^3 = \dfrac{4}{3 \cdot 1000 } \pi \cdot 165.49^3 = 18984.5 \ \text{dm}^3
S=4πr2=4π165.492100=3441.5 dm2S = 4 \pi r^2 = \dfrac{ 4\pi \cdot 165.49^2}{100} = 3441.5 \ \text{dm}^2



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
Do you want to convert area units?
Do you want to convert length units?
Do you know the volume and unit volume, and want to convert volume units?
Pythagorean theorem is the base for the right triangle calculator.

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

Next similar math problems:

  1. Sphere
    cone_sphere_center_1 Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
  2. Spheres in sphere
    Spheres_in_sphere How many spheres with a radius of 15 cm can fits into the larger sphere with a radius of 150 cm?
  3. Gasholder
    gas_holder The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
  4. Pyramid a+h
    jehlan_1 Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
  5. Tin with oil
    konzerva Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
  6. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
  7. Permille of alcohol
    heart I have 2 per mille of alcohol in my blood. How many milliliters is it when I have 5 liters of blood?
  8. Bottles
    flasa_1 The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
  9. Cylindrical tank 2
    watertank_3 If a cylindrical tank with volume is used 12320cm raised to the power of 3 and base 28cm is used to store water. How many liters of water can it hold?
  10. 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?
  11. Newtonmeters
    kluc-skrutky The driver loosened the nut on the car wheel with a wrench that held 20 cm from the axis of the bolt. He acted on the key with a force of 320N. At what moment did he act on the bolt?
  12. Casey
    ham Casey bought a 15.4 pound turkey and an 11.6 pound ham for thanksgiving and paid $38.51. Her friend Jane bought a 10.2 pound turkey and a 7.3 pound ham from the same store and paid $24.84. Find the cost per pound of turkey and the cost per pound of ham.
  13. A candle
    candles A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How
  14. 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?
  15. Boys and money
    money_12 270 USD boys divided so that Peter got three times more than Paul and Ivan has 120 USD more than than Paul. How much each received?
  16. An animal shelter
    cat An animal shelter spends $5.50 per day to care for each bird and $8.50 per day to care for each cat. Nicole noticed that the shelter spent $283.00 caring for birds and cats on Wednesday. Nicole found a record showing that there were a total of 40 birds an
  17. 925 USD
    money_22 Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them?