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# [Smart Math] Geometry Problem 11

Here’s and example of a SMART MATH problem for GEOMETRY.

### Problem

A large cube is formed from the material obtained by melting three smaller cubes of side 3, 4 and 5 cms. What is the ratio of the total surface areas of the smaller cubes and the large cube?

1. 4 : 3
2. 3 : 2
3. 25 : 27
4. 27 : 20
5. 32 : 15

### The Usual Method

Surface area of cube with side 3 cms = $6\times 3^{2}=6\times 9=54$ cms2

Surface area of cube with side 4 cms = $6\times 4^{2}=6\times 16=96$ cms2

Surface area of cube with side 5 cms = $6\times 5^{2}=6\times 25=150$ cms2

Hence, total surface area of the smaller cubes = 54 + 96 + 150 = 200 cms2

Volume of cube with side 3 cms = $3^{3}=27$ cms3

Volume of cube with side 4 cms = $4^{3}=64$ cms3

Volume of cube with side 5 cms = $5^{3}=125$ cms3

Hence, total volume of the smaller cubes = 27 + 64 + 125 = 216 cms3

Hence, side of the larger cube = $\sqrt[3]{216}=6$ cms

Hence, surface area of the larger cube = $6\times 6^{2}=6\times 36=216$ cms2

Hence, ratio of surface areas = 200 : 216

i.e. 25 : 27

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.