Question 831408: what dimensions of a tin can of volume 54 pie cm^3 should be produced if the required height is equal to the diameter of its base
Answer by Elomeht(22)   (Show Source):
You can put this solution on YOUR website! 1. The volume of the can (assumed cylindrical) is given by the formula:
V = PI (r^2) h where r is the radius of the base and h is the height
2. Since the height is equal to the diameter of the base (i.e. 2r), we can modify
the formula to read:
V = PI (r^2)2r = 2PI (r^3)
3. We are told that the volume of the can is 54PI cubic centimeters, so we can put:
54PI = 2PI (r^3)
4. From the above, 27 = (r^3), so r = 3
5. The diameter of the base is therefore 6, which is the same as the height
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