A sphere is inscribed in a cube that has a surface area of 24 m². A second cube is then inscribed within the sphere. What is the surface area in square metres of the inner cube?
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Solution

Given that surface area of the original cube = 24 units.
$∴$ Length of each side of the cube $= \sqrt{\frac{24}{6}} = 2 u n i t s$ units.
The radius of the biggest possible sphere that can be kept inside the cube of each side 2 Units.
$= (\frac{2}{2}) = 1 u n i t$
Now, the diagonal of the second cube inscribed in the sphere = Diameter of sphere
$\Rightarrow \sqrt{3}$ (length of each side of second cube) = 2 units.
$\Rightarrow$ Length of each side of second cube $= \frac{2}{\sqrt{3}}$ unit
$∴$ Surface area of the inner cube = $6 \times (\frac{2}{\sqrt{3}}) = 6 \times \frac{4}{3} = 8 u n i t s$

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A sphere is inscribed in a cube that has a surface area of 24 m2. A second cube is then inscribed within the sphere. What is the surface area in square metres of the inner cube? ___

A sphere is inscribed in a cube that has a surface area of 24 m². A second cube is then inscribed within the sphere. What is the surface area in square metres of the inner cube?
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