OG-11.191

[rishijhawar]

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. of all such canisters that could be used, What is the radius, in inches, of the one that has maximum volume?
a)3
b)4
c)5
d)6
e)8
[spoiler]OA.B. Though an old post, still not 100% clear why radius can't be 5.[/spoiler]

[winniethepooh]

As the insides of the box has been given we can calculate the radii given for each combination of the opening of the box..
we are just interested in the height and the diameter of the biggest possible cylinder that can be placed in the box.
In this sum there are three possibilities:
1. top of the box = 6 and 8 = Area of the cylinder will be: 3 square*10*pie = 90 pie
2. top of the box = 8 and 10 = Area of the cylinder will be: 4 square*6*pie = 96 pie
3. top of the box = 6 and 10 = Area of the cylinder will be: 3 square*8*pie = 72 pie
Maximum radii is given by 2 possibility.Hence, answer is 4.

Note:The radii will be of the lowest side in the opening as bigger then that wont fit in.
The height will be the dimension not considered
The best way to solve is thinking about a rectangular box!

[rishijhawar]

Hey Winnie, thanks for a great explanation.
Somehow I am struggling to digest the explanation" The radii will be of the lowest side in the opening as bigger then that wont fit in". I have found similar kind of explanation in some places, but still unable to grasp it totally.
I tried using a diagram, but not 100% sure how to crack this kind of sums on the D day.
Could you please help me here.
Thanks

[newgmattest]

https://www.manhattangmat.com/forums/dif ... t1113.html

[Whitney Garner]

Hey Winnie, thanks for a great explanation.
Somehow I am struggling to digest the explanation" The radii will be of the lowest side in the opening as bigger then that wont fit in". I have found similar kind of explanation in some places, but still unable to grasp it totally.
I tried using a diagram, but not 100% sure how to crack this kind of sums on the D day.
Could you please help me here.
Thanks

Another way to think about it:

Volume = height * Pi * (radius)^2

So let us simply attack each height.

If height 10, then the circles will rest on the 6x8 rectangular sides. The longest diameter would be 6 inches, because longer would fall outside of the 6 dimension (see image)



So volume would be 10*Pi*(3)^2

Rather than multiply this out - let's list all the options:

Height, Face
10, 6x8
8, 6x10
6, 8x10

So the 3 volumes would be (in the order listed above):
10*Pi*(3)^2, 8*Pi*(3)^2, 6*Pi*(4)^2

Rather than multiply, factor out (they all have Pi, 2 and 3)
5*3, 4*3, 2*8
15, 12, 16
Height 6 gives the greatest volume, so radius is 4.


Whit

[winniethepooh]

Well explained, Whit!
Hey, its a pure logic based question Rishi, so I think you should practice more of these kinds. Make notes for things you don't understand or that which took a lot of time to understand, keep solved notes. Keep reviewing, seek advice!

[rishijhawar]

Thanks, will do.

[rishijhawar]

Whit, thanks for wonderful explanation. thats really helpful.