[25 : 18] A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm si

For Competitive Exams

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?

2 : 1

3 : 2

25 : 18

27 : 20

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, $a^3 $= 216 a = 6 cm.

ஃ Required ratio = $(\dfrac{6 x (3^2 + 4^2 + 5^2)}{6 x 6^2}) = \dfrac{50}{36} $= 25 : 18

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