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Geometry | OG 12

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Geometry | OG 12

by [email protected] » Wed Sep 26, 2012 7:55 pm
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindricalcanister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

I am not able to understand why cant we take 10 as the length so that radius becomes 5 and height is 8. giving us the maximum volume?
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by Anurag@Gurome » Wed Sep 26, 2012 8:15 pm
[email protected] wrote:The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindricalcanister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

I am not able to understand why cant we take 10 as the length so that radius becomes 5 and height is 8. giving us the maximum volume?
Volume of cylinder = (pi) * radius² * height of cylinder
If the cylinder is placed on 6 in by 8 in. face, then it's maximum radius is 6/2 = 3 and volume will be (pi) * 3² * 10 = 90(pi)
If the cylinder is placed on 6 in by 10 in. face, then it's maximum radius is 6/2 = 3 and volume will be (pi) * 3² * 8 = 72(pi)
If the cylinder is placed on 8 in by 10 in. face, then it's maximum radius is 8/2 = 4 and volume will be (pi) * 4² * 6 = 96(pi)

We can see that the volume is maximum when radius = 4 in.

The correct answer is B.
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