Question
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?
Answer: Option B
:
B
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B
Given that surface area of the original cube = 24 units.
∴ Length of each side of the cube =√246= 2 units.
The radius of the biggest possible sphere that can be kept inside the cube of each side 2 units.
= 22 = 1 unit.
Now, the diagonal of the second cube inscribed in the sphere = Diameter of sphere.
⇒√3 (length of each side of second cube) = 2 units.
⇒Length of each side of second cube =2√3 unit
∴ surface area of the inner cube = 6 x(2√3)2
= 6×43= 8 units
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