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

**Problem**

**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?

- 4 : 3
- 3 : 2
- 25 : 27
- 27 : 20
- 32 : 15

**The Usual Method**

[contentblock id=google-adsense-post]

Surface area of cube with side 3 cms = cms^{2}

Surface area of cube with side 4 cms = cms^{2}

Surface area of cube with side 5 cms = cms^{2}

Hence, total surface area of the smaller cubes = 54 + 96 + 150 = 200 cms^{2}

Volume of cube with side 3 cms = cms^{3}

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

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

Hence, total volume of the smaller cubes = 27 + 64 + 125 = 216 cms^{3}

Hence, side of the larger cube = cms

Hence, surface area of the larger cube = cms^{2}

Hence, ratio of surface areas = 200 : 216

i.e. 25 : 27

**(Ans: 3)**

*Estimated Time to arrive at the answer = 60 seconds.*

**Using Technique**

[contentblock id=google-adsense-post]

Add squares of 3, 4 and 5 to get 9 + 16 + 25 = 50.

50 is a factor of the total surface areas of the three smaller cubes and hence 50 or its factor should be one of the values in the proportion. Only option ‘3’ has the factor of 50; 25, so option ‘3’ has to be the answer.

**(Ans: 3)**

*Estimated Time to arrive at the answer = 10 seconds.*

[starrater tpl=10]

[contentblock id=smartmath-blockquote]