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A rectangular tank needs to be coated with insulation. The tank has

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A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 03:04
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A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2.5 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?

A. $1000
B. $1300
C. $1500
D. $1700
E. $1900

Kudos for a correct solution.
[Reveal] Spoiler: OA

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A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 03:58
Bunuel wrote:
A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2.5 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?

A. $1000
B. $1300
C. $1500
D. $1700
E. $1900

Kudos for a correct solution.


Let, Length (L) = 4 feet
Width (B) = 5 feet
Height (H) = 2.5 feet

Total Surface Area of Rectangular Solid = 2(LB + BH + LH)

i.e. Total Surface Area of the tank to be painted = 2*(4*5 + 5*2.5 + 4* 2.5) = 2*(20+12.5+10) = 85 square feet

Cost of Painting 85 square feet @$20 per square feet = 85*20 = $1700

Answer: option D
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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 05:29
Dimensions of the tank = 4X5X2.5

Total Surface Area of Cuboid = 2(lb + bh + lh) = 2(20 + 12.5 + 10) = 85 sq.ft.

Cost of insulating 1 sq.ft = $20, so total cost = 85*20 = $1700. Ans D.
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A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 06:20
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The tank has 6 surfaces of which there are two sides of the same dimensions.

Upper and lower part: (5*4) * 2 = 40 sq. ft
Left and right side: (2,5*4) * 2 = 20 sq. ft
Front and back side: (2,5*5) *2 = 25 sq. ft

40+20+25 = 85 sq. ft

85 * 20 (cost per square foot of insulation) = 1.700 USD

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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 06:25
Bunuel wrote:
A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2.5 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?

A. $1000
B. $1300
C. $1500
D. $1700
E. $1900

Kudos for a correct solution.


total SA=2(4*5+2.5*5+4*2.5)=85..
cost per sq ft=20..
total cost=85*20=1700
ans D
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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 08:53
total surface area = 2(lb+bh+lh)
=2(4*5+5*2.5+4*2.5)
=85

cost = 85*20 = 1700

Answer D
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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 01 Jul 2015, 18:56
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f(\(\frac{x}{20}\)) = surface area, and surface area = \(2(4*5 + 4*2.5 + 5*2.5) = 85\). Thus,
A. $1000 = 50. Too low.
B. $1300 = 65. Too low.
C. $1500 = 75. Too low.
D. $1700 = 85. Surface area. Correct
E. $1900 = 95. Too high.

Thanks,
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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 06 Jul 2015, 03:49
Bunuel wrote:
A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2.5 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?

A. $1000
B. $1300
C. $1500
D. $1700
E. $1900

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

To find the surface area of a rectangular solid, sum the individual areas of all six faces:

Image

Covering the entire tank will cost 85 x $20 = $1,700.

Answer: D.

[Reveal] Spoiler:
Attachment:
2015-07-06_1447.png
2015-07-06_1447.png [ 18.37 KiB | Viewed 1866 times ]

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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

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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 06 May 2017, 17:25
Bunuel wrote:
A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2.5 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?

A. $1000
B. $1300
C. $1500
D. $1700
E. $1900


We can first determine the surface area of the tank:

SA = 2(w x l) + 2(w x h) + 2(h x l)

SA = 2(4 x 5) + 2(4 x 2.5) + 2(2.5 x 5)

SA = 40 + 20 + 25

SA = 85

Since the surface area is 85 square feet, and each square foot costs 20 dollars, the total cost is 85 x 20 = 1700 dollars.

Answer: D
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Re: A rectangular tank needs to be coated with insulation. The tank has [#permalink]

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New post 28 Sep 2017, 06:33
What if the question said swimming pool instead of a tank, will we still add the area of the top ? ( or go with logic as swimming pool is always open)

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Re: A rectangular tank needs to be coated with insulation. The tank has   [#permalink] 28 Sep 2017, 06:33
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