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# A circular tub has a band painted around its circumference

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Math Expert
Joined: 02 Sep 2009
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A circular tub has a band painted around its circumference  [#permalink]

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26 Aug 2012, 03:19
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Difficulty:

5% (low)

Question Stats:

87% (00:48) correct 13% (01:01) wrong based on 804 sessions

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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.

Practice Questions
Question: 30
Page: 277
Difficulty: 600

Attachment:

TUB.png [ 14.01 KiB | Viewed 14578 times ]

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

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31 Aug 2012, 03:10
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SOLUTION:

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.

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

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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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31 Aug 2012, 03:25
Zinsch123 wrote:
I don't think, this is 650 level. Seems pretty easy to me.

We even don't have to calculate anything here.

Changed the difficulty level to 600. Thank you.
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Re: A circular tub has a band painted around its circumference  [#permalink]

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31 Aug 2012, 03:44
1
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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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) ?

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

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03 Jun 2015, 02:45
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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) ?

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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09 Aug 2016, 13:36
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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.

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

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07 Jul 2017, 14:19
Area of a cylinder = $$2 * \pi r(r+h)$$

Statement 1) Tells us x=0.5
We dont know what is r................Insufficient

Statement 2) Tells us h=1
We still dont know the value of r................Insufficient

Combining 1 and 2, we still dont know what is r. Hence, answer is E
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Re: A circular tub has a band painted around its circumference  [#permalink]

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27 Jul 2017, 21:02
I have a question here. So the tub in the figure is a cylinder right?? So if the question had been to find the surface area of the cylinder rather than finding the SA of the painted band then the statements would be sufficient
??
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Re: A circular tub has a band painted around its circumference  [#permalink]

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11 Mar 2018, 23:02
Bunuel can you refer some good quality similar questions? Thanks.
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Re: A circular tub has a band painted around its circumference  [#permalink]

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11 Mar 2018, 23:38
Bunuel can you refer some good quality similar questions? Thanks.

Check 3-D Geometry Questions in our Special Questions Directory.
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Re: A circular tub has a band painted around its circumference  [#permalink]

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22 Apr 2019, 09:36
Clearly to find the surface area we need the radius of the circular cross-section which is not given in either 1 or 2.

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Re: A circular tub has a band painted around its circumference   [#permalink] 22 Apr 2019, 09:36
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