Sphere

The surface of the sphere is 12100 cm², and the weight is 136 kg. What is its density?

Correct answer:

h =  1086.6 kg/m³

Step-by-step explanation:

$$\begin{gathered} S=12100{\text{cm}}^2\to {\text{m}}^2=12100\mathrm{/}10000{\text{m}}^2=1.21{\text{m}}^2 \\ m=136\text{ kg } \\ S=4\pi r^2 \\ r=\sqrt{{\displaystyle \frac{S}{4\pi }}}=\sqrt{{\displaystyle \frac{1.21}{4\cdot 3.1416}}}\doteq 0.3103\text{ m } \\ V={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 0.3103^3\doteq 0.1252{\text{m}}^3 \\ h=m\mathrm{/}V=136\mathrm{/}0.1252=1086.6{\text{kg/m}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Iron sphere
  Iron sphere has weight 100 kg and density ρ = 7600 kg/m³. Calculate the volume, surface and diameter of the sphere.
• Canister
  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?
• 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
• 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?
• 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.
• Sphere A2V
  The surface of the sphere is 241 mm². What is its volume?
• 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
• Canopy
  Mr Peter has a metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs to paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m²?
• Cube 6
  Volume of the cube is 216 cm³, calculate its surface area.
• 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.
• 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.
• 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?
• Balls
  Three metal balls with volumes V₁=71 cm³ V₂=78 cm³ and V₃=64 cm³ melted into one ball. Determine it's surface area.
• 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).
• 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.
• 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.
• 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