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

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

Volume of the large cube = (3 3 + 4 3 + 5 3 ) = 216 cm 3 Let the edge of the large cube be a. So, a3 = 216 ⟹ a = 6 cm. ∴ Required ratio = ❨ 6 x (32 + 42 + 52) ❩ = 50 = 25 : 18. 6 x 62 36

2 : 1
3 : 2
25 : 18
27 : 20

Correct Answer: 25 : 18

Explanation:

Volume of the large cube = (3 ³ + 4 ³ + 5 ³ ) = 216 cm ³

Let the edge of the large cube be a.

So, a³ = 216 ⟹ a = 6 cm.

∴ Required ratio =	❨	6 x (3² + 4² + 5²)	❩	=	50	= 25 : 18.
		6 x 6²			36

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