When a rectangular label, 21.5 centimeters long, is wrapped

Question

When a rectangular label, 21.5 centimeters long, is wrapped around the curved surface of a solid circular cylinder with its shorter ends overlapping, it exactly covers the curved surface. What is the volume of the cylinder in cubic centimeters, if the thickness of the label is ignored?

(1) The label overlap is 0.5 centimeter.
(2) The width of the label is 7.5 centimeters.

My answer to this question was correct but just wondering if you guys see some discrepancy in this problem like I did. Let me know what you guys think, I'll post my observation later. :-D

stoolfi · Answer

Volume of a cylinder= Base * height
To find the base, all we need is the radius, diameter, or circumference.

A tells us the circumference, but not the height.
B tells us the height, but not the circumference.

Both together seem sufficient.


 if you guys see some discrepancy in this problem like I did 
Nope. I hate it when I miss the discrepancy!

dj · Answer

answer: C

volume = pi*r^2*h
a) circumference 2*pi*r = 21
will get r
b) width of label = h

together these are sufficient

wonder_gmat · Answer

Ok first of all, I see discrepancy in the problem where it says "it exactly covers the curved surface" yet Statement (1) says it overlaps 0.5 cm.

I got the answer correct but if you really think about it, we don't really need to consider Statement (1) if it weren't for the discrepancy. We know the height of the label from the actual question, all we need is the width, which is provided by Statement (2). So the logically correct answer should be B, not C. The stupidity in Statement (1) makes it important here. Amazing...
:drunk

Praetorian · Answer

wonder..

where'd you get this question

you get B?

wonder_gmat · Answer

I got it from GMATPlus. Well I would have answered B to be logically correct but after seeing the detail in Statement (1), I answered C. And it is correct, the OA is C. But I think this is just a stupid question... trying to play the word games.

jlgdr · Answer

We are asked to find the volume. We need to know the radius and the height.

We know that 2 (pi) r h = 21.5 
But we need two things:
1) We have the overlap issue
2) We need to know the split between r and h since it will affect our volume formula

Let's hit the statements

1: This solves the overlap stuff, but we are missing the split
2: Solves the split but doesn't tell me about the overlap

Looks like its going to be a C here

Hope it helps
J

hdwnkr · Answer

Volume = Pi * r * r * H

r = radius
H =height

Statement 1 gives the radius. No height. Insuff.

Statement 2 gives the height. No radius. Insuff.

Both together : Sufficient Hence, C

anila1632 · Answer

what is meant by ' with its shorter ends overlapping'..... does it mean width

davedekoos · Answer

Hi Anila,

With a rectangle, you will have two longer sides and two shorter sides. When the rectangular sticker is wrapped around the cylinder, it is done in such a way that the long sides wrap the circumference of the cylinder, and the short sides line up with the height of the cylinder. Because the long sides of the sticker are longer than the circumference of the cylinder, the sticker will overlap itself. When the problem states "... with its shorter ends overlapping...", it means that the short sides of the cylinder will overlap as per the diagram below.

Attachment:

Cylinder Sticker.png [ 8.03 KiB | Viewed 4205 times ]

Let me know if it's still unclear.

Cheers

anila1632 · Answer

thank u.. its clear now

sairam595 · Answer

Can someone explain how C is correct answer!!

Senthil7 · Answer

Volume is 2 * pi * (radius)^2 * height of cylinder.

here height of cylinder will be the length of the rectangular sheet. We need the radius which, when visualized using the question steam, would be width of the rectangular sheet that wraps the cylinder /2. But since the wrap is completed only after a certain extent of overlap we need both statements as one gives overlap and another the width.

Radius = (width of rectangular sheet - overlap) / 2

hence we need both the statements =>  Choice C.

Bunuel · Answer

Discussed here: when-a-rectangular-label-21-5cm-long-is-wrapped-around-the-curved-su-267598.html?fl=similar

When a rectangular label, 21.5 centimeters long, is wrapped

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