Helpw with a 10th grade math problem?

Question

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


Choices...
A)3
B)6
C)8
D)9
E)12

Answer 1

SA of cube = 24 = 6a^2
a=2
radius of sphere = 1
let a1 be lenght of a side of the cube inscribed, then we find a1 using pythagoras theorem: a1^2+a1^2=2^2 (2r is a diagonal of base of cube) 2a1^2=4; a1^2=2
therefore a = sqrt 2
SA of cube1 = 6*2 = 12

To emy: how one side can be L and another Lsqrt2 if this is a cube.

Answer 2

I shall call them bigger cube and smaller one
fo the bigger cube :
s.a. = 24 m^2
s.a. of cube = 6L^2
Such that L is edge length of cube
6L^2 = 24
L^2 = 24/6
L^2 = 4 square root both
L = 2m
The edge lenght is equal to diameter of sphere
dimaeter of sphere = 2 m
this dimaeter of shpere represent the also the diagonal of the inner cube
the diagonal length can be calculated through pythagora's
formin right angled triangle inside that cube whose :
hypotenuse = d ( diagonal of sphere )
side = L another side = Lroot 2
d^2 = L^2 + (Lroot2)^2
2L^2 + L^2 = 4
3L^2 = 4
L^2 =4/3
L = 2/root3
that L is side of inner cube
s.a. inner cube = 6L^2
= 6( 2/root3 )^2
= 6 * 4/3 =8 m^2
hope that helppps

Answer 3

the answer is d. i am 100 percent sure. good luck

Answer 4

B)

Answer 5

E
Please give me best answer thanks!