Wall thickness

The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.

Result

h =  0.607 cm

Solution:

D=40 cm R=D/2=40/2=20 cm  m=25 kg=25 1000 g=25000 g ρ=8.45 g/cm3  m=ρV V=m/ρ=25000/8.452958.5799 cm3  V=V1V2 V=43 π R343 π (Rh)3 3 V4πR3=(Rh)3  Rh=R33 V4π3 h=RR33 V4π3=202033 2958.57994 3.141630.60680.607 cmD=40 \ \text{cm} \ \\ R=D/2=40/2=20 \ \text{cm} \ \\ \ \\ m=25 \ kg=25 \cdot \ 1000 \ g=25000 \ g \ \\ ρ=8.45 \ \text{g/cm}^3 \ \\ \ \\ m=ρ V \ \\ V=m/ρ=25000/8.45 \doteq 2958.5799 \ \text{cm}^3 \ \\ \ \\ V=V_{1}-V_{2} \ \\ V=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ R^3-\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ (R-h)^3 \ \\ \dfrac{ 3 \cdot \ V }{ 4 \pi } - R^3=-(R-h)^3 \ \\ \ \\ R-h=\sqrt[3]{ R^3 - \dfrac{ 3 \cdot \ V }{ 4 \pi } } \ \\ h=R -\sqrt[3]{ R^3 - \dfrac{ 3 \cdot \ V }{ 4 \pi } }=20 -\sqrt[3]{ 20^3 - \dfrac{ 3 \cdot \ 2958.5799 }{ 4 \cdot \ 3.1416 } } \doteq 0.6068 \doteq 0.607 \ \text{cm}



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 know the volume and unit volume, and want to convert volume units?
Tip: Our Density units converter will help you with the conversion of density units.
Do you want to convert mass units?

Next similar math problems:

  1. Hollow sphere
    sphere2 The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
  2. Hollow sphere
    Xmas_ball Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm3), if the inner diameter is 14 cm and wall thickness is 3 mm.
  3. Hollow sphere
    sphere_2 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 density of steel is 7850 kg/m3
  4. Hemispherical hollow
    odsek The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
  5. Plasticine ball
    p_balls Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls
  6. Volume of ball
    ball1_5 Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
  7. Iron ball
    damper_sphere The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
  8. Gasholder
    gas_holder The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
  9. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  10. Sphere fall
    sphere How many percent fall volume of sphere if diameter fall 10×?
  11. Sphere growth
    sphere How many times grow volume of sphere if diameter rises 10×?
  12. Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8
  13. Solid in water
    inwater The solid weighs in air 11.8 g and in water 10 g. Calculate the density of the solid.
  14. 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?
  15. The edge of a cube
    cubes How much does the edge of a cube of 54.9 cm3 measure?
  16. Cuboid edges in ratio
    cuboid_11 Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
  17. 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?