Answers (1)
r = radius of the sphere
d = 2r = diameter of the sphere = space diagonal of the cube
a = side length of the cube
3a^2 = d^2
a^2 = (1/3) * d^2
a = d * sqrt(1/3)
a = 2r * sqrt(1/3)
Area of one side:
a^2 = 4r^2 * (1/3)
a^2 = (4/3) * r^2
The cube has six sides:
6a^2 = 8r^2
Now, have fun with the weird specification of your radius ...
In the last bit a typo sneaked in. Here's the CORRECTION:
The final equation was: The cube has six sides:
6a^2 = 8r^2 ;;; plug in the values
6 * 12^2 = 8 * (6 * sqrt (3))^2
6 * 144 = 8 * 36 * 3
864 = 864
So, the surface area of the largest possible cube made out of a wooden sphere of radius 6×1.732 (6 * sqrt (3)) is 864 (whatever-length-unit)^2.
Well, the radius given is 6 * 1.732, which is a workable approximation for
r = 6 * sqrt (3).
As shown above
a = 2r * sqrt (1/3) ;;; plug in r = 6 * sqrt (3)
a = 12 * sqrt (3 * 1/3)
a = 12
r = 12 / (2 * sqrt (1/3))
r = 6 * sqrt (3)
The final equation was: The cube has six sides:
6a^2 = 8r^2 ;;; plug in the values
6 * 12^2 = 8 * (6 * (1/3))^2
6 * 144 = 8 * 36 * 3
864 = 864
So, the surface area of the largest possible cube made out of a wooden sphere of radius 6×1.732 (6 * sqrt (3)) is 864 (whatever-length-unit)^2.