GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Aug 2018, 00:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A circular tub with radius 1/2 meter and height 1/4 meter has a band

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47983
A circular tub with radius 1/2 meter and height 1/4 meter has a band  [#permalink]

### Show Tags

08 Dec 2017, 03:51
00:00

Difficulty:

35% (medium)

Question Stats:

55% (01:16) correct 45% (02:08) wrong based on 32 sessions

### HideShow timer Statistics

A circular tub with radius 1/2 meter and height 1/4 meter has a band painted around its circumference, as shown above. What is the surface area of the painted band in square meters?

(A) π/20
(B) 5π/12
(C) 5π
(D) 10π
(E) 15π

Attachment:

2017-12-08_1441_003.png [ 8.68 KiB | Viewed 523 times ]

_________________
Manager
Joined: 24 Nov 2016
Posts: 152
Re: A circular tub with radius 1/2 meter and height 1/4 meter has a band  [#permalink]

### Show Tags

08 Dec 2017, 06:04
Bunuel wrote:

A circular tub with radius 1/2 meter and height 1/4 meter has a band painted around its circumference, as shown above. What is the surface area of the painted band in square meters?

(A) π/20
(B) 5π/12
(C) 5π
(D) 10π
(E) 15π

Attachment:
2017-12-08_1441_003.png

Height of band is 5 cm = 1/20 meter

Cylinder Surface Area: $$2πr^2+2πrh$$

Band Surface Area: $$2πr*height.of.band.around = 2π(1/2)(1/20) = π/20$$

SC Moderator
Joined: 22 May 2016
Posts: 1907
A circular tub with radius 1/2 meter and height 1/4 meter has a band  [#permalink]

### Show Tags

08 Dec 2017, 15:45
Bunuel wrote:

A circular tub with radius 1/2 meter and height 1/4 meter has a band painted around its circumference, as shown above. What is the surface area of the painted band in square meters?

(A) π/20
(B) 5π/12
(C) 5π
(D) 10π
(E) 15π

Attachment:
2017-12-08_1441_003.png

The surface area of the band equals the band's height * (circumference of cylinder's base): $$h * 2\pi r$$

Band's height:
$$5cm * \frac{1meter}{100cm}=\frac{5}{100}m=\frac{1}{20}m$$

Band's surface area, in square meters:
$$h * 2\pi r$$
$$\frac{1}{20} * (2)\pi (\frac{1}{2})$$
$$\frac{\pi}{20}$$

* This problem has two wrinkles: you use only part of a cylinder's surface area formula, and the given height of the cylinder does not matter.
Surface area of a cylinder:
$$(2\pi r)(2) + (2\pi r)(h) = (4\pi r + 2\pi r h)$$
$$(2\pi r)(2)$$ is the circular area of the cylinder's top and bottom, i.e., (area of circle * 2)
$$(2\pi r)(h)$$ is the area of the rectangle (if "unrolled). One length of the rectangle is the cylinder's circumference. The other length of the rectangle is the height of cylinder.

In this case, the band's surface area has nothing to do with the first expression (areas of top and bottom). And the band's area, though calculated the same as the rectangle's (circumference * height), has nothing to do with the given height of the rectangle, because the band's height in centimeters must be translated to a fraction of a meter anyway.

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

A circular tub with radius 1/2 meter and height 1/4 meter has a band &nbs [#permalink] 08 Dec 2017, 15:45
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.