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Math Expert V
Joined: 02 Sep 2009
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The statue of liberty is approximately 150 feet tall from the base to  [#permalink]

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Question Stats: 24% (01:37) correct 76% (01:27) wrong based on 68 sessions

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The statue of liberty is approximately 150 feet tall from the base to the tip of the torch. A scale model is built that is 3 feet tall. If painting the scale model requires 5 cans of paint, approximately how many cans of paint would be required to paint the real Statue of Liberty? (Assume that paint is used at the same rate on the real statue as it is on the model.)

A. 50
B. 250
C. 2,500
D. 10,000
E. 12,500

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Math Expert V
Joined: 02 Aug 2009
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Bunuel wrote:
The statue of liberty is approximately 150 feet tall from the base to the tip of the torch. A scale model is built that is 3 feet tall. If painting the scale model requires 5 cans of paint, approximately how many cans of paint would be required to paint the real Statue of Liberty? (Assume that paint is used at the same rate on the real statue as it is on the model.)

A. 50
B. 250
C. 2,500
D. 10,000
E. 12,500

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The painting would depend on the AREA and here we have just height.
So, I would assume that all the dimensions are in the same ratio, and let me take a square ....
The ratio of area is SQUARE of the ratio of sides, so sides = 3:150
The ratio of Area = 3*3:150*150=1:2500
So if 1 square unit requires 5 cans, 2500 sq unit would require 5*2500=12500 cans.

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Re: The statue of liberty is approximately 150 feet tall from the base to  [#permalink]

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Here if we assume figure to be a cube, then we would get a different answer. could you please clarify, how can i restrict my understanding to 2d figure?
Math Expert V
Joined: 02 Aug 2009
Posts: 8327
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Aviral1995 wrote:

Here if we assume figure to be a cube, then we would get a different answer. could you please clarify, how can i restrict my understanding to 2d figure?

Hi even if it is a cube, we will be looking for surface area and not volume.
So surface area =6a^2=6*3^2 and this requires 5 cans
The Statue of Liberty surface area = 6*150^2, so can required =5*6*150^2/(6*3^2)=5*3^2*50^2/3^2=5*50^2=12500
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Re: The statue of liberty is approximately 150 feet tall from the base to  [#permalink]

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Bunuel wrote:
The statue of liberty is approximately 150 feet tall from the base to the tip of the torch. A scale model is built that is 3 feet tall. If painting the scale model requires 5 cans of paint, approximately how many cans of paint would be required to paint the real Statue of Liberty? (Assume that paint is used at the same rate on the real statue as it is on the model.)

A. 50
B. 250
C. 2,500
D. 10,000
E. 12,500

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We must recall that if the heights of a 3D object and its model are in a ratio of n to 1, then the ratio of their surface areas is n^2 to 1 (and the ratio of their volumes is n^3 to 1).

For example, if we have a cube with side length of 3 cm, then the surface area (for painting just the outside) is 3^2 x 6 = 54 sq cm. Now consider another cube with side length twice as long, 6 cm. Now, the surface area is 6^2 x 6 = 216 sq cm. Note that 216 is 4 times as great as 54, so the ratio of their surface areas is n^2 : 1, or 4 : 1. Thus, if we need 1 can to paint the surface of the small cube, we will need 4 cans to paint the larger cube’s surface.

Similarly, the ratio of the heights of the Statue of Liberty and its model is 150 to 3, or 50 to 1. So n = 50, and thus the ratio of their surface areas is 2500 : 1. Since we need to paint the surface area of the Statue of Liberty, we need 50^2 = 2500 times as many cans of paint. Since the model needs 5 cans of paint, the real structure will need 2500 x 5 = 12,500 cans of paint.

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