Kostka

Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?

Result

p =  36.755 %

Solution:

r=6 cm D=2⋅ r=2⋅ 6=12 cm u=D=12 cm  u=3a a=u/3=12/3≐4 3 cm≐6.9282 cm  V1=a3=6.92823≐192 3 cm3≐332.5538 cm3 V2=43⋅ π⋅ r3=43⋅ 3.1416⋅ 63≐904.7787 cm3  p=100⋅ V1V2=100⋅ 332.5538904.7787≐36.7553≐36.755%r=6 \ \text{cm} \ \\ D=2 \cdot \ r=2 \cdot \ 6=12 \ \text{cm} \ \\ u=D=12 \ \text{cm} \ \\ \ \\ u=\sqrt{ 3 } a \ \\ a=u / \sqrt{ 3 }=12 / \sqrt{ 3 } \doteq 4 \ \sqrt{ 3 } \ \text{cm} \doteq 6.9282 \ \text{cm} \ \\ \ \\ V_{1}=a^3=6.9282^3 \doteq 192 \ \sqrt{ 3 } \ \text{cm}^3 \doteq 332.5538 \ \text{cm}^3 \ \\ V_{2}=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 6^3 \doteq 904.7787 \ \text{cm}^3 \ \\ \ \\ p=100 \cdot \ \dfrac{ V_{1} }{ V_{2} }=100 \cdot \ \dfrac{ 332.5538 }{ 904.7787 } \doteq 36.7553 \doteq 36.755 \%

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