A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?
OA: 200pie
Source: Manhattan GMAT Geometry 4th edition, pg. 49.
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LalaB
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the largest volume is possible, if the height is 8, and the rest (10 and 12) are the legs.
so, the volume =5^2*8=25*8=200
so, the volume =5^2*8=25*8=200
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Thrills4ever
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Anurag@Gurome
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Volume of cylinder = pi * r² * h.HG10 wrote:A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?
OA: 200pie
Source: Manhattan GMAT Geometry 4th edition, pg. 49.
For maximum volume, radius should be maximum because it has a square power.
This is possible if we take the base of cylinder as the base of the box which is 12*10.
Then the diameter is 10 for the cylinder, as it has to be lesser of 10 and 12.
Or radius is 10/2 = 5 and height is 8.
So volume is pi * 5² * 8 = 200pi.
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Troika
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Guys, thank you for your responses.
I just have one question, i.e. if radius should me maximum for maximum volume, why select r=10/2, why not r=12/2 and h=10 instead of h=8?
I just have one question, i.e. if radius should me maximum for maximum volume, why select r=10/2, why not r=12/2 and h=10 instead of h=8?
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LalaB
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u better try to draw ur desired figure. if u do so, u will find out that it is impossible to have two sides 10 and 12, and get 12/2,since the max value of ur side is 10.HG10 wrote:Guys, thank you for your responses.
I just have one question, i.e. if radius should me maximum for maximum volume, why select r=10/2, why not r=12/2 and h=10 instead of h=8?
Happy are those who dream dreams and are ready to pay the price to make them come true.(c)
In order to succeed, your desire for success should be greater than your fear of failure.(c)
In order to succeed, your desire for success should be greater than your fear of failure.(c)
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Troika
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Thank you, LalaB and Anurag@Gurome for your solutions and explanations.
@LalaB, thanks for pointing out the dimensional limitations.
@LalaB, thanks for pointing out the dimensional limitations.
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