Quantitative Aptitude Ques 291
Question: A large cube is formed by melting three smaller cubes of 3 cm, 4 cm and 5 cm side. What is the ratio of the total surface areas of the small cubes and the larger cube?
Options:
A) 2 : 1
B) 3 : 2
C) 25 : 18
D) 27 : 20
Show Answer
Answer:
Correct Answer: C
Solution:
- Volume of largest cube $ =3^{3}+4^{3}+5^{3} $ $ =27+64+125=216,cm^{3} $
$ \therefore $ Side of largest cube $ =\sqrt[3]{216}=6,cm $ Total surface area of small cube
$ \therefore $ Required ratio $ \text{=}\frac{Total,surface,area,of,small,cube}{Total,surface,area,of,largest,cube} $ $ \text{=},\frac{6\times {{(3)}^{2}}+6\times {{(4)}^{2}}+6\times {{(5)}^{2}}}{6\times {{(6)}^{2}}} $ $ =,\frac{9+16+25}{36}=\frac{50}{36}=\frac{25}{18}=25:18 $
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