Question 587207
We know that side length of a cube is 8 inches.

Volume of the cube = {{{ (side length)^3 }}}
     V(cube) =  {{{ 8^3 }}}
     V(cube) = 512 cubic inches

WE know that the radius of the cylinder is r = 4 inches and let the height of the cylinder be h inches.
Volume of the cylinder = π{{{ r^2*h }}}
V(cylinder) = {{{ pi*4^2*h }}}
V(cylinder) = 16πh

Since the volume of cube and cylinder are same, so

V(cylinder) = V(cube)
or   16πh = 512
or    πh = 512/16  {Dividing both the sides by 16}
or  πh = 32
or h = 32/π  inches 

If we wish to get the decimal value fo h, we can use the standard value of π = 3.14

Therefore,  h = 32/π = 32/3.14
or  h = 10.189
or  h = 10.2 inches (approximately)



Hope this helps~!