SOLUTION: A sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume of the sphere to the nearest cubic inch. Thanks!

Algebra ->  Volume -> SOLUTION: A sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume of the sphere to the nearest cubic inch. Thanks!      Log On


   

Question 618928: A sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume of the sphere to the nearest cubic inch. Thanks!
Found 2 solutions by mananth, Alan3354:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Since the sphere is circumscribed by the cube the radius of the sphere = 4 in
Volume of sphere = 4/3 pi r^3
Volume = 4/3 * 22/7 * 4^3
= 268 cu.in

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume of the sphere to the nearest cubic inch.
---------------
The diameter of the sphere = the cube's long diagonal between 2 vertices not on the same face.
d+=+sqrt%288%5E2+%2B+8%5E2+%2B+8%5E2%29+=+sqrt%28192%29
r+=+d%2F2+=+sqrt%2848%29
--------
For the sphere:
Vol+=+4%2Api%2Ar%5E3%2F3+=+4%2Api%2A48%2Asqrt%2848%29%2F3+=+64%2Api%2Asqrt%2848%29 cubic inches