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Updated on: 10 Jan 2021, 11:57
Originally posted by willget800 on 25 Apr 2006, 18:54.
Last edited by Bunuel on 10 Jan 2021, 11:57, edited 3 times in total.
Last edited by Bunuel on 10 Jan 2021, 11:57, edited 3 times in total.
Edited the question.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylinder that can be placed inside the box?
A. \(180\pi\)
B. \(200\pi\)
C. \(300\pi\)
D. \(320\pi\)
E. \(450\pi\)
A. \(180\pi\)
B. \(200\pi\)
C. \(300\pi\)
D. \(320\pi\)
E. \(450\pi\)
Since the radius of the cylinder is squared to obtain its volume, the radius should be the maximum possible radius in order for the cylinder to achieve its maximum volume.
Point to keep in mind while selecting the maximum possible radius: The diameter should be <= two of the largest sides of the rectangle. If one selects the largest side of the rectangle as the diameter, then the cylinder won't fit into the other side of the rectangle. Refer Figure.
cylinder in rectangle.JPG [ 10.15 KiB | Viewed 51158 times ]
As a rule of thumb, in such problems, select the second largest side as the diameter (note that it is the diameter and one has to calculate the radius by dividing by 2 before calculating the volume). And the left alone smallest side will be the height of the cylinder (as you need the two largest sides to enclose the bottom of the cylinder the only choice left out for height is the smallest side).
Point to keep in mind while selecting the maximum possible radius: The diameter should be <= two of the largest sides of the rectangle. If one selects the largest side of the rectangle as the diameter, then the cylinder won't fit into the other side of the rectangle. Refer Figure.
Attachment:
cylinder in rectangle.JPG [ 10.15 KiB | Viewed 51158 times ]
02 Mar 2012, 03:19
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Ashamock
Why cant we have radius =6 and height = 10 making the volume 360 Pi ?
Dimensions of the box are 12*10*8 inches if radius of a cylinder is 6 then its diameter is 12 and it won't fit on any face of a box. For example it can not fit on 12*10 face of the box since diameter=12>10=side.
Complete solution:
A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylcinder that can be placed inside the box?
\(volume_{cylinder}=\pi{r^2}h\)
If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*12=192\pi\);
If the cylinder is placed on 8*12 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*10=160\pi\);
If the cylinder is placed on 10*12 face then it's maximum radius is 10/2=5 and \(volume==\pi*{5^2}*8=200\pi\);
So, the maximum volume is for \(200\pi\).
Answer: B.
Similar question to practice: https://gmatclub.com/forum/the-inside-di ... 28053.html
Hope it helps.
