Dimensions of a rectangular wooden box

umaa

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

ans(b)

Please explain me how is b correct.

sudhir3127 · Posted: Thu Jul 17, 2008 1:45 am Post subject:

consider the cuboid...it has 3 different rectangles - 6x8, 8x10 and 6x10 tht form the faces of cuboid.

volume of a cylinder is pi*r^2*h

if the cylinder rests on the 6x8 rectangle, then the max. diameter it can hv is 6 inches and max. height is 10 inches..hence volume = 90pi

consider 8x10 face, max diameter = 8 in. and max vol = 96pi

consider 6x10 face, max diameter = 6 in. and max vol = 72pi

hence, max vol = 96pi when diameter = 8 in.

hence the radius = 4 inches

Chitts · Posted: Thu Jul 17, 2008 1:51 am Post subject:

First you have to identify the number of canisters possible. Here with the values you have provided the number would be 3. One canister will be in the base of dimension 6x8 and height 10, the other would be 8x10 with height 6 and last 10x6 with height 8.
Now consider the first can dimensions written above. The maximum radius of the canister can be 3 (6/2). This can be easily know by drawing a rectangle and trying to adjust a circle with the highest possible radius. After you know the radius the volume would be "pie.3(square).10" which is 90pie.
Similarly the other two canisters in question would have volume 96pie (pie.4(square).6) and 72pie (pie.3(square).8).

So maximum volume is 96pie. Hence the radius of that canister is 4.

Hope my explanation is clear for you to understand... Smile

parallel_chase

ildude02

ildude02 · Posted: Thu Jul 17, 2008 3:01 pm Post subject:

agemroy · Posted: Fri Jul 18, 2008 8:45 am Post subject:

The question states "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".

This means that the height of the cylinder is equal to the height of the box.

Hence, we cannot consider the diameter to be 10.

olpre4 · Posted: Sun Aug 10, 2008 6:14 pm Post subject: H x L X W

The problem quotes the dimensions 6" x 8" x 10"?

How are we suppose to know which dimension is height?

Is height quoted at the end or the beginning?

Because in this problem it is quoted in the beginning as 6", but in problem #176 (of the Official GMAT Guide 11th Edition) it is quoted at the end.

I wish GMAT would be consistent in its dimension quoting conventions.

Can someone tell me the best way to approach this type of issue on the GMAT.

Senator 153 · Posted: Sun Aug 10, 2008 6:30 pm Post subject:

This question is awesome. Best way to approach it: first, draw one 3-D box to give yourself an idea of what you're looking at and label the edges according to length. Write the formula for the volume of the cylinder: V = Length * PI * radius^2

From the formula, you'll see that increasing the radius is the best way to increase the cylinder's volume.

Trouble is, and this is the catch: you can't have "the biggest radius" of 5 in this particular case because the biggest face is? 10x8, not 10x10. You still want the biggest radius, so you go with 10x8 and your radius is 4. The volume is L*PI*(4)^2. Lenth is six, so volume is 96Pi. You could draw another box where the length of the cylinder is 10, but your radius would drop to three (face is 8x6) and you'd be stuck at 90Pi for the volume.

Comments: agemroy, we can't use a diameter of 10 but not for the reason you've specified. The cylinder literally won't fit in the box. olpre4, it actually doesn't matter which dimension we assign height to.

olpre4 · Posted: Sun Aug 10, 2008 6:59 pm Post subject: Thanks

I see. Thanks!!

Martian421 · Posted: Mon Sep 08, 2008 5:29 am Post subject:

awesome explanations..

Thanks everyone for posting this!