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GRE Prep Club Team Member
Joined: 20 Feb 2017
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A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A c
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31 Mar 2021, 22:27
31 Mar 2021, 22:27
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50% (01:25) correct
50% (02:10) wrong based on 4 sessions
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A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
A. 4
B. 5
C. 6
D. 8
E. 10
A. 4
B. 5
C. 6
D. 8
E. 10
Re: A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A c
[#permalink]
02 Apr 2021, 01:48
02 Apr 2021, 01:48
Let's take the volume equation for cylindrical gas tank.
Volume \(= pi * r^2 * h\), where volume is dependent on two variables: r = radius, and h = height.
Volume will be maximum when the radius is maximum because r is squared while h is not. So, let's think of ways when r could be maximum.
In the rectangular crate, if you consider 8 x 10 or 8 x 12 sides to place the circular bottom, diameter can only stretch to 8. Whereas if you consider 10 x 12 side, the diameter can stretch to 10, giving us a maximum radius of 5.
Hence, B is the correct answer.
Volume \(= pi * r^2 * h\), where volume is dependent on two variables: r = radius, and h = height.
Volume will be maximum when the radius is maximum because r is squared while h is not. So, let's think of ways when r could be maximum.
In the rectangular crate, if you consider 8 x 10 or 8 x 12 sides to place the circular bottom, diameter can only stretch to 8. Whereas if you consider 10 x 12 side, the diameter can stretch to 10, giving us a maximum radius of 5.
Hence, B is the correct answer.
gmatclubot
Re: A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A c [#permalink]
02 Apr 2021, 01:48
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