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.

E

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

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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