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Question

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?

Options:
A .  2 : 1
B .  3 : 2
C .  25 : 18
D .  27 : 20
Answer: Option C

Volume of the large cube = (33 + 43 + 53) = 216 cm3.


Let the edge of the large cube be a.


Let the edge of the large cube be a.


So, a3 = 216     \(\Rightarrow\)      a = 6 cm.


So, Required ratio =  \(\left(\frac{6\times(3^{2}\times4^{2}\times5^{2})}{6\times6^{2}}\right)=\frac{50}{36}= 25:18.\)


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