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. Copper sheet
    cuplech The copper plate has a length of 1 m, width 94 cm and weighs 9 kg. What is the plate thickness, if 1 m3 weighs 8715 kg?
  2. Copper plate
    plech Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg
  3. 3d printer
    filament 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
  4. Orlík hydroelectric plant
    1280px-Orlík_1 The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the
  5. Cu thief
    trolleywire_1 The thief stole 122 meters copper wire with cross-section area of 95 mm2. Calculate how much money gets in the scrap redemption, if redeemed copper for 5.5 eur/kg? The density of copper is 8.96 t/m3.
  6. A car
    car_31 A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
  7. Pump
    pumpa What power has a pump output to move 4853 hl of water to a height of 31 m for 8 hours?
  8. Angled cyclist turn
    cyclistTurn The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
  9. Friction coefficient
    car What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
  10. Car crash
    car1_7 On the road, with a maximum permitted speed of 60 km/h, there was a car crash. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, as
  11. Water level
    bazen_11 How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
  12. Density of the concrete
    beton_1 Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
  13. Traffic collision
    crash When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village
  14. Hydrostatic force
    water3_5 What hydrostatic force is applied to an area of 30 cm2 in water at a depth of 20 m? (Water density is 1000 kg/m3)
  15. Basic form
    time_3 Expressed the ratios of values in the basic form: 0,5 t : 1,2 kg 200 l : 0,15 m3 12 t : 3600 kg 500 kg : 2,5 t 0,9 kg : 500 g 3,6 m : 240 cm 1200 mm : 2,4 m 300 l : 0,3 m3 6 min 30 s : 900 s
  16. Tower model
    tower 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-dig
  17. Canister
    kanister Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg?