A right cone is to be placed within a rectangular box so that the cone stands upright when the box is placed on one of its sides. If the dimensions of the box are 2 inches by 2 inches by 4 inches, then what is the greatest possible volume of such a cone?
A. (2/3)
B. (4/3)
C. 2
D. (8/3)
E. 4
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A. (2/3)
B. (4/3)
C. 2
D. (8/3)
E. 4
[Reveal] Spoiler:
Since the radius is limited in any case by at least one side of 2, the greatest volume will be achieved by maximizing the height. Since that is the case, the base of the box is 2x2, so the cone has a base radius of 1 and a base area of r=1=. The height is 4, thus the Maximum Cone Volume=1/3r2H=(4/3)
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