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

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Math Expert
Joined: 02 Sep 2009
Posts: 50610
A circular tub with radius 1/2 meter and height 1/4 meter has a band  [#permalink]

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08 Dec 2017, 02:51
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:27) correct 44% (02:18) wrong based on 38 sessions

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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 572 times ]

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

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08 Dec 2017, 05:04
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: $$2πr*height.of.band.around = 2π(1/2)(1/20) = π/20$$

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Joined: 22 May 2016
Posts: 2094
A circular tub with radius 1/2 meter and height 1/4 meter has a band  [#permalink]

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08 Dec 2017, 14:45
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.
A circular tub with radius 1/2 meter and height 1/4 meter has a band &nbs [#permalink] 08 Dec 2017, 14:45
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