SOLUTION: Either a right cylinder or a cube can be formed by bending the same rectangular sheet of aluminum. Neither the cylinder nor the cube will have a bottom or top. Find the volume of t

Algebra ->  Surface-area -> SOLUTION: Either a right cylinder or a cube can be formed by bending the same rectangular sheet of aluminum. Neither the cylinder nor the cube will have a bottom or top. Find the volume of t      Log On


   

Question 701028: Either a right cylinder or a cube can be formed by bending the same rectangular sheet of aluminum. Neither the cylinder nor the cube will have a bottom or top. Find the volume of the cylinder if the volume of the cube is 27pi/4 cm3. Plaese show me step by step .Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Either a right cylinder or a cube can be formed by bending the same rectangular sheet of aluminum.
Neither the cylinder nor the cube will have a bottom or top.
Find the volume of the cylinder if the volume of the cube is 27pi/4 cm3.
:
let x = one side of the cube
then the sheet of aluminum will be 4x by x
and the volume of cube:
x^3 = %2827pi%29%2F4
:
The cylinder,
4x = the circumference of the cylinder
and
x = the height
Use the circumference to find the radius of the cylinder
2pi%2Ar+=+4x
pi%2Ar+=+2x
r+=+%282x%29%2Fpi
Find the volume of cylinder: A+=+pi%2Ar%5E2%2Ah, replacing r and h
V = pi%2A%28%282x%29%2Fpi%29%5E2%2Ax
V = pi%2A%28%284x%5E2%29%2Fpi%5E2%29%2Ax
cancel pi
V = %28%284x%5E3%29%2Fpi%29
We know from the vol of the cube that x^3 = %2827pi%29%2F4
V = %28%284%2827pi%29%2F4%29%2Fpi%29
Cancel the 4
V = %28%2827pi%29%29%2Fpi
Cancel pi
V = 27 cu/cm is the volume of the cylinder
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Hey student, did this actually make sense? It's the end of the day for me and I am not thinking very well. Hope it does. C