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

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

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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.
[Reveal] Spoiler: OA

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

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New post 02 Jul 2015, 02:14
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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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New post 02 Jul 2015, 02:36
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)

Answer:: Option 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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New post 03 Jul 2015, 08:05
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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New post 04 Jul 2015, 11:31
C is correct
surface ares = 2*pi*r (r+h) = 102 Pi

Buckets = 102 pi /10 pi = 10.2
rounding off to 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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New post 06 Jul 2015, 06:06
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.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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Re: Jane has to paint a cylindrical column that is 14 feet high and that   [#permalink] 14 Sep 2017, 05:37
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