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:

$$\begin{gathered} m=100\text{ kg } \\ h=7600{\text{kg/m}}^3 \\ m=hV \\ {V}_1={\displaystyle \frac{m}{h}}={\displaystyle \frac{100}{7600}}={\displaystyle \frac{1}{76}}\doteq 0.0132{\text{m}}_3 \\ V=V_1\to {\text{dm}}^3=V_1\cdot 1000{\text{dm}}^3=0.0132\cdot 1000{\text{dm}}^3=13.158{\text{dm}}^3={\displaystyle \frac{250}{19}}{\text{dm}}^3=13.1579{\text{dm}}^3 \end{gathered}$$

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

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

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