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rectangular solid inside cylinder

by Uva@90 » Sat Aug 08, 2015 11:04 pm
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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by [email protected] » Sun Aug 09, 2015 9:12 am
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.

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by Uva@90 » Sun Aug 09, 2015 9:05 pm
[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.

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Rich
Hi 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,
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Uva
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by nikhilgmat31 » Mon Aug 10, 2015 4:37 am
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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by DavidG@VeritasPrep » Mon Aug 10, 2015 4:44 am
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
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.)
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by DavidG@VeritasPrep » Mon Aug 10, 2015 4:53 am
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
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.)
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by [email protected] » Mon Aug 10, 2015 9:14 am
Hi Uva@90,

YES, you are correct. Nicely done.

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by Uva@90 » Mon Aug 10, 2015 7:16 pm
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
Nikhil,

Normally Regular polygon has the greater Area.

For Example Square > Rectangle
and Equilateral Triangle > any other Triangle.

Thanks.
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Uva.
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by nikhilgmat31 » Tue Aug 11, 2015 3:30 am
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.
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