Sphere

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

Result

h =  1086.6 kg/m3

Solution:

S=12100 cm2=12100/10000 m2=1.21 m2 m=136 kg  S=4 πr2  r=S4π=1.214⋅ 3.1416≐0.3103 m  V=43⋅ π⋅ r3=43⋅ 3.1416⋅ 0.31033≐0.1252 m3  h=m/V=136/0.1252≐1086.6434≐1086.6 kg/m3S=12100 \ cm^2=12100 / 10000 \ m^2=1.21 \ m^2 \ \\ m=136 \ \text{kg} \ \\ \ \\ S=4 \ \pi r^2 \ \\ \ \\ r=\sqrt{ \dfrac{ S }{ 4 \pi } }=\sqrt{ \dfrac{ 1.21 }{ 4 \cdot \ 3.1416 } } \doteq 0.3103 \ \text{m} \ \\ \ \\ V=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r ^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 0.3103 ^3 \doteq 0.1252 \ \text{m}^3 \ \\ \ \\ h=m/V=136/0.1252 \doteq 1086.6434 \doteq 1086.6 \ \text{kg/m}^3

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