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28 Dec 2021, 07:30
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
44% (01:58) correct
56%
(01:59)
wrong
based on 18
sessions
History
Date
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Not Attempted Yet
Some glass vases in the shape of a right circular cylinder are to be shipped. For shipment they are to be packed into rectangular boxes. To ensure no damage, the vase must sit upright in the box and fit snugly against the top and bottom of the box. If the shipping box has dimensions of 6 inches by 8 inches by 10 inches, what is the minimum volume of a vase that could be packed in such a box?
(A) \(50\pi\)
(B) \(60\pi\)
(C) \(72\pi\)
(D) \(90\pi\)
(E) \(100\pi\)
Are You Up For the Challenge: 700 Level Questions
(A) \(50\pi\)
(B) \(60\pi\)
(C) \(72\pi\)
(D) \(90\pi\)
(E) \(100\pi\)
Are You Up For the Challenge: 700 Level Questions
17 Jan 2022, 16:06
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Bunuel
If the only requirement is that it "fit snugly against the top and bottom", that means the height needs to be 6, 8 or 10, but the radius could be very close to zero, and the minimum volume is zero.
I imagine the question means for the cylinder to also touch two opposite walls of the box, or in other words, it means that the diameter must also equal one of the box's dimensions. Since the volume of a cylinder is π r^2 h, then we want to make r as small as we can, because we're squaring it, and we can make the diameter the dimension of length 6, and the radius 3. We then just want to choose the smaller of the other two dimensions as our height, to minimize our volume, so the height will be 8, and the volume will be π * 3^2 * 8 = 72π.
