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# Jane has to paint a cylindrical column that is 14 feet high and that

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Math Expert
Joined: 02 Sep 2009
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Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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02 Jul 2015, 01:39
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Difficulty:

45% (medium)

Question Stats:

66% (01:08) correct 34% (01:18) wrong based on 116 sessions

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Jane has to paint a cylindrical column that is 14 feet high and that has a circular base with a radius of 3 feet. If one bucket of paint will cover $$10\pi$$ square feet, how many full buckets does Jane need to buy in order to paint the column, including the top and bottom?

A. 9
B. 10
C. 11
D. 12
E. 13

Kudos for a correct solution.

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Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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02 Jul 2015, 03:14
3
Concept : Total Surface area of a cylinder (2 bases + curved surface) = 2πrh + 2πr*r --------- (1)

Using 1,
Total surface area to be painted = 2π*3*14 + 2π*3*3 = 102π -------------- (2)

We need 1 bucket to paint 10π area ------------------ (3)

From 2 & 3,
To paint 102π = 102π/10π = 10.2 buckets are required.

Thus we need to buy 11 paint buckets in all !!
Hence C
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Re: Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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02 Jul 2015, 03:36
Bunuel wrote:
Jane has to paint a cylindrical column that is 14 feet high and that has a circular base with a radius of 3 feet. If one bucket of paint will cover $$10\pi$$ square feet, how many full buckets does Jane need to buy in order to paint the column, including the top and bottom?

A. 9
B. 10
C. 11
D. 12
E. 13

Kudos for a correct solution.

The Surface Area to be painted = 2πr^2 + 2πrh = 2π*3(3+14) = 102π

Buckets of Paint needed = Total Area to be painted / Area painted by one bucket = 102π / 10π = 10.2 = 11 Bucket (Because 10 buckets are insufficient so we need 11)

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Re: Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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03 Jul 2015, 09:05
surface ares = 2*pi*r (r+h) = 102 Pi

Buckets = 102 pi /10 = 10.2

Hence we need 11 buckets ...
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Re: Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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04 Jul 2015, 12:31
C is correct
surface ares = 2*pi*r (r+h) = 102 Pi

Buckets = 102 pi /10 pi = 10.2
rounding off to 11
Math Expert
Joined: 02 Sep 2009
Posts: 47898
Re: Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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06 Jul 2015, 07:06
Bunuel wrote:
Jane has to paint a cylindrical column that is 14 feet high and that has a circular base with a radius of 3 feet. If one bucket of paint will cover $$10\pi$$ square feet, how many full buckets does Jane need to buy in order to paint the column, including the top and bottom?

A. 9
B. 10
C. 11
D. 12
E. 13

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

The surface area of a cylinder is the area of the circular top and bottom, plus the area of its wrapped-around rectangular third face.

Top & Bottom: $$A = \pi r^2 = 9\pi$$
Rectangle: $$A = 2\pi r * h = 84\pi$$

The total surface area, then, is $$9\pi + 9\pi + 84\pi = 102 \pi$$ ft2. If one bucket of paint will cover $$10\pi$$ ft^2, then Jane will need 10.2 buckets to paint the entire column. Since paint stores do not sell fractional buckets, she will need to purchase 11 buckets.

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Re: Jane has to paint a cylindrical column that is 14 feet high and that  [#permalink]

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14 Sep 2017, 06:37
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Re: Jane has to paint a cylindrical column that is 14 feet high and that &nbs [#permalink] 14 Sep 2017, 06:37
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