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.

Correct answer:

h =  0.6068 cm

Step-by-step explanation:

$$\begin{gathered} D=40\text{ cm } \\ R=D\mathrm{/}2=40\mathrm{/}2=20\text{ cm } \\ m=25\text{ kg}\to \text{ g}=25\cdot 1000\text{ g}=25000\text{ g } \\ \rho =8.45{\text{g/cm}}^3 \\ m=\rho V \\ V=m\mathrm{/}\rho =25000\mathrm{/}8.45\doteq 2958.5799{\text{cm}}^3 \\ V=V_1-V_2 \\ V={\displaystyle \frac{4}{3}}\cdot \pi \cdot R^3-{\displaystyle \frac{4}{3}}\cdot \pi \cdot (R-h{)}^3 \\ {\displaystyle \frac{3\cdot V}{4\pi }}-R^3=-(R-h{)}^3 \\ R-h=\sqrt[3]{R^3-{\displaystyle \frac{3\cdot V}{4\pi }}} \\ h=R-\sqrt[3]{R^3-{\displaystyle \frac{3\cdot V}{4\pi }}}=20-\sqrt[3]{20^3-{\displaystyle \frac{3\cdot 2958.5799}{4\cdot 3.1416}}}=0.6068\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• Hollow sphere
  The 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 the density of steel is 7850 kg/m³
• Iron sphere
  Iron sphere has weight 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface and diameter of the sphere.
• Hollow sphere
  Calculate the weight of a hollow stříbrné sphere (density 10.5 g/cm³) if the vnitřní diameter is 15 cm and wall thickness is 1 mm.
• Hollow sphere
  The volume of the hollow ball is 3432 cm³. What is its internal radius when the wall thickness is 3 cm?
• Brass tube
  The outer perimeter of brass tube (ρ = 8.5 g/cm³) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
• Sphere
  The surface of the sphere is 12100 cm², and the weight is 136 kg. What is its density?
• Brass ball
  What is the weight of a hollow brass ball, the outer diameter of which is 16 cm and the wall thickness is 2 cm, while the density of brass is ϱ = 8.5 g
• Plastic pipe
  Calculate the plastic pipe's weight with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m³.
• The square
  The square oak board (with density ρ = 700 kg/m³) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?
• Cone from cube
  From a wooden block, 20 cm high was the turned largest possible cone. Calculate its weight if you know that the density of wood was 850 kg/m³
• Sphere floating
  Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm³. (Instructions: Calculate the average sphere density and compare it with the water density. )
• The prison ball
  Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.
• Seawater
  Seawater has a density of 1025 kg/m³, ice 920 kg/m³. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
• Steel tube
  The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m³. Calculate its length if it weighs 15 kg.
• Brass sphere
  Find the weight of a brass ball with an outer radius of 12 cm, a wall thickness of 20 mm if the brass's density is 8.5 g/cm³.
• CuZn
  Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m³, the zinc density is 7130 kg/m³. Calculate how many kg of copper and zinc a cube contains.
• Copper plate
  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