A cylindrical tank has height of 10 feet and base with radius of 6 feet. if the thickness of the tank's sides is negligible , what is the volume , in cubic feet, of the largest rectangular solid that could be placed inside the tank?
A) 60
B) 360
C) 240 root (3)
D) 360 root (2)
E) 720
OA E
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rectangular solid inside cylinder
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Hi Uva@90,
I'm going to give you a couple of hints so that you can attempt this question again:
1) The largest rectangular solid that can be placed in a cylinder will have a SQUARE base.
2) Draw a picture of what you would see if you looked "down" into the cylinder (you'll see a circle with a square in it). The diagonal of the square will equal the diameter of the circle.
GMAT assassins aren't born, they're made,
Rich
I'm going to give you a couple of hints so that you can attempt this question again:
1) The largest rectangular solid that can be placed in a cylinder will have a SQUARE base.
2) Draw a picture of what you would see if you looked "down" into the cylinder (you'll see a circle with a square in it). The diagonal of the square will equal the diameter of the circle.
GMAT assassins aren't born, they're made,
Rich
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Uva@90
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Hi Rich,[email protected] wrote:Hi Uva@90,
I'm going to give you a couple of hints so that you can attempt this question again:
1) The largest rectangular solid that can be placed in a cylinder will have a SQUARE base.
2) Draw a picture of what you would see if you looked "down" into the cylinder (you'll see a circle with a square in it). The diagonal of the square will equal the diameter of the circle.
GMAT assassins aren't born, they're made,
Rich
Using your info here is my shot,
Since Base is Square Each side would be 6root(2)(since diagonal = diameter=12 )
so volume = 6root(2) * 6roo(2) * 10 = 720
Is my approach correct ?
Thanks,
Regards,
Uva
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nikhilgmat31
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Am I correct to say
For a given Area
Square has the maximum Area with minimum Perimeter.
Rectangle has the maximum Perimeter with minimum Area.
Please suggest.
lets say a area of 4 sqcm.
side of square = 2
Perimeter = 4 * 2 = 8
side of rectangle can be = 2 & 2 with Perimeter = 2(2 + 2) = 8
side of rectangle can be = 4 & 1 with Perimeter = 2(4 + 1) = 10
For a given Area
Square has the maximum Area with minimum Perimeter.
Rectangle has the maximum Perimeter with minimum Area.
Please suggest.
lets say a area of 4 sqcm.
side of square = 2
Perimeter = 4 * 2 = 8
side of rectangle can be = 2 & 2 with Perimeter = 2(2 + 2) = 8
side of rectangle can be = 4 & 1 with Perimeter = 2(4 + 1) = 10
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DavidG@VeritasPrep
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It is true that for a fixed perimeter, the rectangle that maximizes the area would be a square. (And remember that all squares are, in fact, rectangles.)Am I correct to say
For a given Area
Square has the maximum Area with minimum Perimeter.
Rectangle has the maximum Perimeter with minimum Area.
Please suggest.
lets say a area of 4 sqcm.
side of square = 2
Perimeter = 4 * 2 = 8
side of rectangle can be = 2 & 2 with Perimeter = 2(2 + 2) = 8
side of rectangle can be = 4 & 1 with Perimeter = 2(4 + 1) = 10
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DavidG@VeritasPrep
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Similarly, if you had two rectangles with equal area, one square and one non-square, the non-square would have the larger perimeter. (Which makes sense. If we took the non-square, kept the perimeter the same, and made it into a square, the area would then increase.)Am I correct to say
For a given Area
Square has the maximum Area with minimum Perimeter.
Rectangle has the maximum Perimeter with minimum Area.
Please suggest.
lets say a area of 4 sqcm.
side of square = 2
Perimeter = 4 * 2 = 8
side of rectangle can be = 2 & 2 with Perimeter = 2(2 + 2) = 8
side of rectangle can be = 4 & 1 with Perimeter = 2(4 + 1) = 10
GMAT/MBA Expert
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Hi Uva@90,
YES, you are correct. Nicely done.
GMAT assassins aren't born, they're made,
Rich
YES, you are correct. Nicely done.
GMAT assassins aren't born, they're made,
Rich
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Uva@90
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Nikhil,nikhilgmat31 wrote:Am I correct to say
For a given Area
Square has the maximum Area with minimum Perimeter.
Rectangle has the maximum Perimeter with minimum Area.
Please suggest.
lets say a area of 4 sqcm.
side of square = 2
Perimeter = 4 * 2 = 8
side of rectangle can be = 2 & 2 with Perimeter = 2(2 + 2) = 8
side of rectangle can be = 4 & 1 with Perimeter = 2(4 + 1) = 10
Normally Regular polygon has the greater Area.
For Example Square > Rectangle
and Equilateral Triangle > any other Triangle.
Thanks.
Regards,
Uva.
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nikhilgmat31
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Thanks Uva it helps.
so a rectangle with a given perimeter has maximum area when it is a SQUARE. (Regular Polygon)
Similarly a regular polygon(or a square) with a given area has minimum perimeter when it is a rectangle.
so a rectangle with a given perimeter has maximum area when it is a SQUARE. (Regular Polygon)
Similarly a regular polygon(or a square) with a given area has minimum perimeter when it is a rectangle.
