Question

Cube A is inscribed in sphere B, which is inscribed in cube C. If the sides of cube A have length 4, what is the volume of cube C? (PLEASE HELP I WILL GIVE BRAINLIEST)

Answer 1

Volume of cube C is L³ = $(4\sqrt{2}) ^{3} = 128\sqrt{2}$

Step-by-step explanation:

We have , Cube A is inscribed in sphere B, which is inscribed in cube C. Side of cube A have length 4 . Since , cube A is inscribed in sphere B , half of Diagonal length of cube A will be the radius of sphere B . We can find it by Pythagoras Theorem, as

$Diagonal^{2} = length^{2} + length^{2}\\Diagonal^{2} = 4^{2} + 4^{2} \\ Diagonal^{2} = 32$

Taking square root both sides, $diagonal = 4\sqrt[]{2}$,

Radius of sphere B is half of diagonal i.e. r = $2\sqrt[]{2}$.

Now , length of cube C is twice the radius of sphere B i.e. L = 2r = $4\sqrt[]{2}$.

∴Volume of cube C is L³ = $(4\sqrt{2}) ^{3} = 128\sqrt{2}$