A sphere has a surface area of 64π. Find the surface area of the largest cube contained in the sphere.?
thanks!!
Update:i want another if you know without applying pythagorean or considering the diameter as 8 units or
diameter equals diagonal which is 8.
can you state some method without this one?
Update 3:any short hand method over there?
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Well the surface area of sphere is 64Л
Let radius be r. Now surface area is 4Л(r^2)=64Л
r^2=16 and r=(+or-)4
But -4 is discarded as length can't be negative.
So radius is 4 and diameter is 8 units.
But diameter is the cube diagonal(main diagonal not any face diagonal)
If side of cube is 's' then diagonal of cube is √3(s).
But diagonal equals diameter of sphere for longest cube.
=>√3(s) = 8
=> s=8/√3
=> s=(8/3)*√3
Hence side of longest cube is (8/3)*√3 units.
I'm not going to do your math for you, but when you realize that the diagonal of the cube is equal to the diameter of the sphere, you will be able to find your answer.