# Cube in a sphere

The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.

Correct result:

a =  13.9 cm

#### Solution:

$V=7253 \ \text{cm}^3 \ \\ V=\dfrac{ 4 }{ 3 } \pi r^3 \ \\ \ \\ r=\sqrt{ \dfrac{ 3 \cdot \ V }{ 4 \pi } }=\sqrt{ \dfrac{ 3 \cdot \ 7253 }{ 4 \cdot \ 3.1416 } } \doteq 12.0082 \ \text{cm} \ \\ \ \\ D=2 \cdot \ r=2 \cdot \ 12.0082 \doteq 24.0163 \ \text{cm} \ \\ \ \\ u=D=24.0163 \doteq 24.0163 \ \text{cm} \ \\ \ \\ u=\sqrt{ 3 } a \ \\ \ \\ a=u/\sqrt{ 3 }=24.0163/\sqrt{ 3 }=13.9 \ \text{cm}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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i am good at this

2 years ago  2 Likes Crazy Butterfly
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