Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface and diameter of the sphere.

Correct answer:

V =  13.1579 dm³
D =  2.9291 dm
S =  26.9531 dm²

Step-by-step explanation:

$$\begin{gathered} m=100\text{ kg } \\ h=7600{\text{kg/m}}^3 \\ m=hV \\ {V}_1={\displaystyle \frac{m}{h}}={\displaystyle \frac{100}{7600}}={\displaystyle \frac{1}{76}}\doteq 0.0132{\text{m}}_3 \\ V=V_1\to {\text{dm}}^3=V_1\cdot 1000{\text{dm}}^3=0.0132\cdot 1000{\text{dm}}^3=13.158{\text{dm}}^3=13.1579{\text{dm}}^3 \end{gathered}$$

$$\begin{gathered} V={\displaystyle \frac{4}{3}}\pi r^3 \\ r=\sqrt[3]{V\cdot {\displaystyle \frac{3}{4\pi }}}=\sqrt[3]{13.1579\cdot {\displaystyle \frac{3}{4\cdot 3.1416}}}\doteq 1.4645\text{ dm } \\ D=2\cdot r=2\cdot 1.4645=2.9291\text{ dm} \end{gathered}$$

$S=4\pi \cdot r^2=4\cdot 3.1416\cdot 1.4645^2=26.9531{\text{dm}}^2$

Try another example

Related math problems and questions:

• Sphere
  The surface of the sphere is 12100 cm², and the weight is 136 kg. What is its density?
• Iron ball
  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.
• 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
• 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.
• 3d printer
  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)
• 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.
• Iron cast
  What is the weight of cast iron with a volume of 3575 cubic centimeters? The density of the cast iron is 7600 kg/m³
• 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
• Cuboid 5
  Calculate the mass of the cuboid with dimensions of 12 cm; 0.8 dm and 100 mm made from spruce wood (density = 550 kg/m³).
• Cu wire
  Copper wire has a length l = 820 m and diameter d = 10 mm. Calculate the weight if density of copper is ρ = 8500 kg/m³. Result round to one decimal place.
• Cube surface and volume
  The surface of the cube is 500 cm², how much cm³ will be its volume?
• Sphere A2V
  The surface of the sphere is 241 mm². What is its volume?
• Area of a cube
  Calculate the surface area of a cube if its volume is equal to 729 cubic meters.
• 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.
• Tower model
  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-digi
• 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
• Oak trunk
  Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.