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chetan2u VeritasKarishma

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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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


Are You Up For the Challenge: 700 Level Questions

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.

Answer: E
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