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The inside dimensions of a rectangular wooden box are 4 meters by 5 m
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26 Sep 2021, 09:43
26 Sep 2021, 09:43
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Question Stats:
40% (01:45) correct
59% (02:32) wrong based on 27 sessions
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The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum 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 drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume?
(A) \(20 \pi\)
(B) \(24 \pi\)
(C) \(25 \pi\)
(D) \(96 \pi\)
(E) \(100 \pi\)
(A) \(20 \pi\)
(B) \(24 \pi\)
(C) \(25 \pi\)
(D) \(96 \pi\)
(E) \(100 \pi\)
Re: The inside dimensions of a rectangular wooden box are 4 meters by 5 m
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26 Sep 2021, 22:34
26 Sep 2021, 22:34
can you please explain?
Re: The inside dimensions of a rectangular wooden box are 4 meters by 5 m
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26 Sep 2021, 23:24
26 Sep 2021, 23:24
2
So you have to choose a diameter and height that yield the biggest volume. (drawing the figure works best)
take height= 4 and diameter=5 (radious will be 5/2=2.5) and with the formula of the volume r^2*pi*H you get 25pi as the solution.
take height= 4 and diameter=5 (radious will be 5/2=2.5) and with the formula of the volume r^2*pi*H you get 25pi as the solution.
