# 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.

Result

h =  1301.534 kg/m3

#### Solution:

$D=15 \ cm \rightarrow m=15 / 100 \ m=0.15 \ m \ \\ m=2.3 \ \text{kg} \ \\ \ \\ r=D/2=0.15/2=\dfrac{ 3 }{ 40 }=0.075 \ \text{m} \ \\ \ \\ V=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r ^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 0.075 ^3 \doteq 0.0018 \ \text{m}^3 \ \\ \ \\ h=m/V=2.3/0.0018 \doteq 1301.5338 \doteq 1301.534 \ \text{kg/m}^3$

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