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dylanl1218
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28 Jul 2021, 11:14
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parkhydel
Since we're given that the box has dimensions of 8X10X12 then that means that there can be multiple different right circular cylinders that could fit in the box. To organize the problem methodically let's hinge each possible cylinder around the height dimension.
(1) If the height of the cylinder equals 11 (i.e. 12 - 1/2 in - 1/2 in)
(2) If the height of the cylinder equals 9
(3) If the height equals 7
For each scenario that means that there can be a DIAMTER of the top and bottom restricted by the remaining two dimensions that are not selected for height.
(1) Two remaining dimensions are 10 and 8, so maximum diameter = 7 (i.e. 8 - 1/2 in - 1/2 in)
(2) Two remaining dimensions are 12 and 8, so maximum diameter = 7 (i.e. 8 - 1/2 in - 1/2 in)
(3) Two remaining dimensions are 12 and 10, so maximum diameter = 9 (i.e. 8 - 1/2 in - 1/2 in)
So scenario three in which the height = 7, and the diameter = 9 maximizes the radius for a radius of 4.5.
Westfolia007
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01 Aug 2021, 09:39
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nick1816 chetan2u Please correct me if I am wrong
If we consider a rectangle with length L and breadth B, the maximum diameter of the circle would be the breadth B that is it can never be more than the breadth. For the given cube, we know that 3 rectangles are formed with 8, 10 and 12. Maximum area will be for 12,10 rectangle and hence the maximum diameter would be 10. But here there is a thickness for the box. So net diameter would be 10- 2*(0.5), since thickness is on both the sides
Net diameter = 9cm or radius = 4.5 cm IMO C
If we consider a rectangle with length L and breadth B, the maximum diameter of the circle would be the breadth B that is it can never be more than the breadth. For the given cube, we know that 3 rectangles are formed with 8, 10 and 12. Maximum area will be for 12,10 rectangle and hence the maximum diameter would be 10. But here there is a thickness for the box. So net diameter would be 10- 2*(0.5), since thickness is on both the sides
Net diameter = 9cm or radius = 4.5 cm IMO C
19 Sep 2021, 05:40
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parkhydel
First of all we need to tweak the dimensions to 7, 9 , 11 to accomdated the 1/2 inch thickness in both sides
Area of the 3 possible cyclinders = pi* (7/2)^2*11
2nd one ...... =pi*(9/2)^2 *11
Area of the 3rd one ............... =pi* 11/2 * 7
Clearly the radiud of the maximum voloumnous cyclinder = 4.5
Therefore IMO C
