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A circular tub has a band painted around its circumference

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A circular tub has a band painted around its circumference [#permalink]

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New post 26 Aug 2012, 03:19
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Attachment:
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A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band?

(1) x = 0.5
(2) The height of the tub is 1 meter.

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A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band?

The surface area of the band is circumference of the band (circumference of the tub) multiplied by the width of the band.

(1) x = 0.5. We know the width of the band but not the circumference. Not sufficient.

(2) The height of the tub is 1 meter. From the height of the tub we cannot get neither the width of the band nor the circumference of the tub. Not sufficient.

(1)+(2) We still cannot get the circumference of the tub. Not sufficient.

Answer: E.
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Re: A circular tub has a band painted around its circumference [#permalink]

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anewbeginning wrote:
How do I recognize the surface area

As Bunuel told it is (Circumference) (x), where x is the width.

Why can't I say that it is equal to ( (pi) * r^2) (x) ?

Please help


If you consider the band in 2 dimensions, you get a rectangle of length equal to the circumference and with of x. So, the area is \((2\pi{r})x\).

\(\pi{r^2})\) is the area of the top and the base of the cylinder and it has nothing to do with the area of the band.
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Re: A circular tub has a band painted around its circumference [#permalink]

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New post 31 Aug 2012, 03:18
I don't think, this is 650 level. Seems pretty easy to me.

We even don't have to calculate anything here.
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Re: A circular tub has a band painted around its circumference [#permalink]

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New post 31 Aug 2012, 03:44
The answer is E since we don't know the radius of the tub.
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Re: A circular tub has a band painted around its circumference [#permalink]

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Re: A circular tub has a band painted around its circumference [#permalink]

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New post 03 Jun 2015, 00:35
How do I recognize the surface area

As Bunuel told it is (Circumference) (x), where x is the width.

Why can't I say that it is equal to ( (pi) * r^2) (x) ?

Please help
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A circular tub has a band painted around its circumference [#permalink]

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New post 09 Aug 2016, 13:36
Bunuel wrote:
Attachment:
TUB.png
A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band?

(1) x = 0.5
(2) The height of the tub is 1 meter.


We are given a cylinder with a shaded band painted around its circumference. We know that the height of the band is x meters, and we also know that the shape of the band is a hollow cylinder (i.e., a cylinder without the top and bottom circular bases). We need to determine the surface area of the band. We know the surface area of a cylinder (when it has the top and bottom circular bases) is:

surface area = 2πr^2 + 2πrh

Notice that the 2πr^2 is the area of the two circular bases of the cylinder (had it been a solid one). However, here the cylindrical band is hollow, thus its surface area is:

surface area = 2πrh

We can replace h with x since that is the height of the band, so we have:

surface area of band = 2πrx

So if we can determine the value of r and x, we can determine the surface area of the band.

Statement One Alone:

x= 0.5

While we have the value of x, without knowing the value of r, we cannot determine the surface area of the band. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The height of the tub is 1 meter.

Knowing the height of the tub does not provide us with the value of x or r. Statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two together we still do not have a value for r and thus cannot determine the value of the surface area of the band.

The answer is E.
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A circular tub has a band painted around its circumference   [#permalink] 09 Aug 2016, 13:36
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