A standard juice box holds 8 fluid ounces. A fluid ounce of liquid occupies 1.8in.^3. Design a cylindrical can that will hold about the same volume as one juice box. What are some possible dimensions of the can?

Question

anonymous · Answer

8 fl oz = (8)1.8 in^3 =14.4 in^3

geometry with least surface area has diameter = height, so

V = (pi/4)(D^2) h = (pi/4)D^3 = 0.785 D^3 = 14.4

D = cube root of (14.4/0.785) = 2.63 inches diameter and also height

check V = (pi/4)( D^2) h = 14.4 cubic inches   yes