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:

$$\begin{gathered} V=7253{\text{cm}}^3 \\ V={\displaystyle \frac{4}{3}}\pi r^3 \\ r=\sqrt[3]{{\displaystyle \frac{3\cdot V}{4\pi }}}=\sqrt[3]{{\displaystyle \frac{3\cdot 7253}{4\cdot 3.1416}}}\doteq 12.0082\text{ cm } \\ D=2\cdot r=2\cdot 12.0082\doteq 24.0163\text{ cm } \\ u=D=24.0163\doteq 24.0163\text{ cm } \\ u=\sqrt{3}a \\ a=u\mathrm{/}\sqrt{3}=24.0163\mathrm{/}\sqrt{3}=13.9\text{ cm} \end{gathered}$$

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Showing 3 comments:

Math student

i am good at this

2 years ago  2 Likes Like

Crazy Butterfly

This is easy.

7 months ago  Like

Wiggly

Maths is good.

25 days ago  Like

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